If we work on the assumption that this law is in place by about 1930, in the medium term I suspect you might have seen more compressed air driven equipment. This could extend the reach of mechanically locked signalling without necessarily having to tame those pesky electrons. In the longer term (say 1960s onward) , the case for rolling out a standard cab signalling system sooner would have been much stronger. Inevitably this would have involved electrical, electronic or perhaps even early processor equipment. To convince a wary legislature to allow this perhaps system safety engineering techniques may have had a bit more impetus in the rail industry sooner.
Complex pneumatic systems might have a similar risk of incorrect connection as wiring, if that was the nature of the initial problem prompting the ban or restriction.
Onboard systems for cab signalling are unlikely to be electric wire-free, where similar 'faulty wiring' problems might apply. I suppose a mitigation might be that most of the complex wiring would be in standard sealed factory-tested modules.
The interesting question here is, if they didn't trust colour light signalling, would they have allowed reliance on track circuits for train detection? Even absolute block really needs electrical circuits though.
If the issue is complexity rather than the use of electricity per se, track circuits are relatively simple systems. Similar with block bells and instruments. Would telephones be allowed?
EDIT: There's a thought. Did anyone ever drive compressed air valves from depression bars?
No idea! Probably wouldn't be practical or cost-effective for train presence/absence detection over longer distance
An electric lamp circuit though, not a safety critical control circuit.
A main aspect lamp circuit is safety-critical in that the filament is proved to be drawing power, and hence assumed illuminated, using a failsafe current sensing relay in series with the load. The relay contacts are used to switch panel status indications in the signal box and are checked in the circuits for the signal in rear which can only show proceed if the signal ahead is proven alight. An earlier oil lamp equivalent used a bi-metalic strip to detect the heat of the flame and switch an electrical status indication circuit.
London Underground took some time to adapt to the wholly electrical interlockings used increasingly on the main line network from the 1950s. They stuck resolutely with mechanical interlockings even into the 1970s using remote-controlled, pneumatically actuated interlocking machines that processed the bulk of the more complex control logic. There was limited relay circuitry clearly to take the outputs from these contraptions and drive colour light signals and point drive circuits (the points themselves were typically pneumatically actuated), as well as electric solenoid locks proving track circuits clear etc, but the most complex wiring was avoided. A common design of this type of machines was the Westinghouse style V frame that used rotating shafts driven by pneumatic actuators. In event of failure of the local punch tape sequence machines, an early form of automatic route setting, and remote control telemetry, the shafts could also be operated manually under instruction from the control room by local operating or technical staff. LU also didn't trust those new-fangled 'miniature' relays adopted by BR, preferring much larger traditional shelf types of a design colloquially known as 'fish tanks'. LU interlocking machine room wiring is also typically much better insulated and protected from mechanical and other damage than the types used by BR.
interlocking machine
www.ltmuseum.co.uk
Description
This machine replaced the lever frames used by signalmen. Its function is to ensure that there is no conflict between the routes set by the points and the signals. This is done both mechanically and electrically. The levers on the front move sideways instead of fore and aft and are normally moved by compressed air, being controlled by the signalman operating a push-button panel. If the air supply were to fail, the signalman can go into the Interlocking Machine Room (IMR) and operate the levers manually. The moving parts of the machine are physically connected so that it is impossible to set up conflicting routes and signals. If a fault occurs in the control system, the mechanical interlocking provides the final line of defence.
