It's actually kind of a complex subject, some of which we are still piecing together. In reality, the signalling systems used in the Met Boxes (and later Posts) changed over time, evolving as technological, political and sociological needs demanded.
In simplest terms, yes there were lights, and yes there were bells.
Originally, the Boxes were equipped with essentially the same system that had been devised for the older, 1896 era Police Telephone Boxes aka Fixed Point Boxes. The prototype for these situated on Cricklewood Broadway started out with just using the bells that came with the wall mounted telephones of the era as the sole signaling device, but it was very quickly realized that a Constable at his fixed point duty position a number of yards away often couldn't hear it ringing over the ambient noise inherent with the busy junction it was located at. So a visual signal was devised whereby whenever the telephone was rung a flag dropped from in front of a lamp so that it could be seen, accomplished by means of a solenoid operated by a latching relay. The flag being coloured meant that when it was tripped it could be seen in the daytime as well, at least if you looked hard enough. All this had to be reset by hand once the signal was answered.
When it came time to design the new, improved Police Boxes in 1928/29, the same arrangement was used, but to start the flashing of an omnidirectional light on top of the Box instead of merely revealing a steady one through a peep hole or window. There were some problems with this rather simple arrangement, however. For one thing, a Constable had to reset the relay after it had been tripped. There was no way for the Station to clear the signal from their end, so when the Station called the Box the light would remain flashing until it was answered (and just picking up the phone wasn't enough, and in fact would apparently trip the relay as well). It would also appear that the regular bells from a GPO bellset (required for the telephone equipment initially used) would have operated at the same time. It's unknown if there was a secondary signal light inside the Box at this point, operating in series with the top light, but possibly not as the bells would have been enough to signal the Constable inside the Box, yet not so loud as to cause concern. On the other hand, another reason for the existence of that internal signal light was as a test that the top light hasn't burned out, as failure for the inside light to illuminate indicated a fault with the circuit (in later years there being a test button inside to check this), but it's not clear the need for this was realized from the start.
Another issue with the system was the lack of feedback at the Station end as to whether the light was operating properly and whether there was a fault on the line. All these deficiencies proved troublesome in practice.
Actually, there were newspaper reports at the time that some members of the public were confused by the signals and did indeed answer the phone in a flashing Box. This wasn't helped early on by at least one newspaper saying the public should stop and answer the phone to help the Police whenever they saw a flashing light atop a Box (there was a lot of misreporting when the Boxes were introduced, much to the Met's consternation). There were also indications that the light went on whenever the telephone receiver was picked up, alerting a nearby Officer that his help might be required by a member of the Public (I don't know if this "feature" remained throughout all of the changes to the system over time, however). Just entering or being in the Box would not turn the beacon light on though - it had to be triggered by the telephone circuit one way or the other.
Note that this top signal light was originally red in colour, using a red tinted glass cylinder or dome slipped over the bulb, all inside the clear glass Fresnel lens. The signal colour wasn't changed to white until the late 1930s, when confusion with the new traffic lights had become an issue. After a great deal of experimentation, the Met decided that white was the simplest and most reliably visible replacement colour for the signal. When the time was deemed right, the entire Met System was changed over in a single day - must have been fun for the Engineering Department removing the tinted cylinders on over 600 Boxes. The flash rate was approximately one second on and one second off, with the telephone bellset's bells following the same cadence, ringing for a second, then off, etc.
The various deficiencies with this first system were soon recognized, and a search undertaken to try to find a better and more reliable method of signaling. It would appear that certain individuals in the Engineering Department of the Met took it upon themselves to do some R&D on this, but their efforts were at first obscured by other developments.
At the same time (1932-33), the GPO had been developing their own speakerphone based system in conjunction with Ericsson and pitched this as a solution to the Met, but though they said they had thoroughly researched the needs of "all" prospective users and fulfilled their every requirement, they had somehow neglected to consult the (by far) largest Police Force in the nation, much to the annoyance of the Met. Regardless, the technical improvements of the system proposed by the GPO were recognized - the ability to initiate and clear signals at will from the Station, have signal receipt verification, in-built line fault detection, etc, so it was determined that a test should be conducted in a single Division, specifically Z Division beginning in early 1934. However, the Met were steadfastly against the idea of speakerphones on the public side of the telephone units, which was the central feature of the GPO/Ericsson system (the GPO using a standard handset only on the inside of a Kiosk, or in a special compartment of a Post, and for Police use only), preferring to use a common instrument accessible from both within and outside the kiosk. This necessitated modifications to the GPO PA1/PA100 System that complicated matters. Further, the GPO system utilized a 3-way party line rather than the single direct line for each Box as had been previously used. All this created delays to installation and testing, with further suggestions for changes from Z Division itself only adding to these.
Finally, by the beginning of 1935 the new system was deemed successful and ordered to be implemented throughout the outer Divisions, beginning with J and S Divisions, which were in the process of being erected. Further changes to the specifications for both the special telephone units and switchboards, combined with production delays, created a bottleneck that took most of 1935 to clear (hence the reason so few Met Boxes were commissioned in 1935). The Divisions already equipped with Boxes were retrofitted with the new system as well, but not only did the telephone line connections need to be completely rewired for Party lines, but the 60+ Mark 1's had to have their telephone cabinets enlarged to accommodate the new special telephone units (big metal boxes modified from the GPO speakerphone jack-in units), which were mounted to the walls of the telephone cupboard. All this meant that the savings promised by the GPO never really materialized.
The new system signaled essentially the same way as far as the Copper on the beat was concerned, but again with tangible improvements in practicality, control and reliability. When the phone was rung by the station the flashing light was triggered as before, but now it could be stopped at will by the station, no longer requiring the Constable to go inside and flip a switch. It should be noted that the Met essentially improved the GPO system they were testing, making changes that were later adopted back into the GPO's full speakerphone systems as an improved model. You see, as originally designed, though the Station could signal a specific Box, when one of the three Boxes called in the switchboard couldn't tell which of the three was calling. The Met's demands resulted in the design of a small automatic telegraph that was actuated when the handset was lifted off the hook that sent a signal that was decoded by the switchboard itself to illuminate a light that identified the Box. Handling multiple calls from a given party line at the same time was still an issue, however.
As part of this system the internal signal light and test button arrangement also appear to have been finalized (one of the things we still need to pin down), probably in lieu of a normal ringing bell since the new units didn't use a bellset, but there is a distinct lack of indication as of 1937 that any allowance was made by the GPO for a big 6" secondary alarm bell like that on the back wall (as seen on Crich and others via photos). The latter appears to instead have been a war time (or preparation for war) measure so that very loud audible signals could be used for long distance signaling instead of flashing lights that might jeopardize the blackout conditions needed during air raids. Subsequently other solutions were implemented for using the lights during the war while making them invisible (or at least significantly less visible) from the air using special hoods and screens, but the (new?) bells continued in use until the end of the system (nominally 1969-1970). A switch was installed so that the bell could be taken off line while the Box was occupied so as not to deafen the Constable or the neighbors, etc., but from what I've seen of the circuitry there was no way for the central Station to selectively signal the light vs the bell.
While all this was going on, the Met's Engineering Department had actually come up with a better solution going back to dedicated lines (party lines were always problematic in practical use), but due to political momentum their "better mousetrap" didn't see the light of day for more than two years, when it formed the basis for the PA350 system implemented in the inner Divisions (which the GPO essentially adopted themselves more than a decade later to replace their aging speakerphone concept). There were a lot of other technical improvements (including the signal only operating as long as the phone rang, not requiring a separate clearing command), but the end effects were essentially the same - signal the Box and it flashed until stopped or answered.
As stated above, Glasgow (and elsewhere) were a bit different. They used the full GPO/Ericsson speakerphone system and had the Bell built into the light from the beginning, though it's unclear how many actually had the optional ringer mechanism installed to use it or if an auxiliary bell might have been installed inside the Box instead.
By the way, in the Met area at least, for the first part of the war the Air Raid Sirens next to the Boxes had to be actuated from inside the Box, a complicated switching arrangement having been installed in those so equipped. Photos of one such setup and the lengthy instructions posted for use makes the Zero G toilet in 2001 look like child's play in comparison. Within the first year or so this was automated so that the Divisional Station could control them remotely, then finally so that they could all be controlled from a central command bunker. Interesting note is that up until the beginning of the full blown air raids in mid-1940, all Boxes were ordered to be manned 24 hours a day as a vital communications link.
Sorry for the long-winded response, but like I said, it's a bit complicated, and some details are still needing to be clarified and/or verified.
