What difference would Thameslink core style mid platform signals make to Clapham Junction (P12 & P13) and East Croydon? Would it cause more problems than it would solve?
Mid-platform signals are a good solution where usually the only thing preventing a train entering the platform is the previous train still occupying the overlap beyond the end of the platform. By the time a train reaches the mid-platform signal, the previous train should have moved on and cleared the overlap and so the mid-platform signal will clear.
The problem with applying this kind of solution at East Croydon is that the overlap beyond the end of the platform is regularly blocked by conflicting routes over the crossover. The mid-platform signal may therefore be unable to clear when a train approaches. It is obviously not a good idea for a passenger train to be stopped for any time half-in half-out the platform.
A better solution would be to provide "closing-up signals" at the entry to the platform, as has been done for south-bound trains (signals 103, 105, etc.). However, if the existing signals reading into the station are not too far from the platforms, so the distance from these signals to the closing-up signals would be fairly small, then the closing-up signals would not give enough benefit to be worthwhile.