Stray currents would be a killer in the complex layouts scattered across South London.
That's only the case if you persist in running 750V DC and 25kV side by side, as every unit will be dual voltage capable by the time this is a serious problem, the simple solution is to either convert the complex layouts to 25kV first, and change back to 750V DC either side of somewhere like Clapham Junction, or you convert the track upto Clapham Junction to 25kV first and switch back to 750V DC on approach.
The complex layout then transitions at Christmas or Easter - DC switched off, AC switched on, testing and commissioning, and job done. I'd prefer Christmas, and if there are any serious show stopping issues, AC off, DC on and we'll try again at Easter.
The stock just needs electric, it doesn't matter if it's 25kV AC or 750V DC, one can be swapped for the other at any time until the 750V DC rail, switchgear and cabling is actually recovered. It's quite different to electrification of non electrified route, where it's all different stock to deal with.
These are all details which will need to be considered in detail in future years, when this becomes a real problem to contend with.