If it were 1995, the optimal solution would have been NiMH batteries
at the side of the track. They can do massive currents in and out, and a few tons of batteries would be enough to fully store the energy of a passenger train stopping from 60 mph to nil inside 30 secs.
NiMH could have been attached directly to the rails.
Today, lithium batteries win for Watts per dollar, and perhaps custom made packs could also be attached directly to the rails.
But a cheaper solution is probably bidirectional inverters, allowing the DC generated by the trains to be fed back into the 3 phase national grid.
Unfortunately, all trains in London today cannot regen into the grid - they can only regen into the rails and hope that some other train on the same rail is accelerating at the same time to use the energy. By my estimates, that only happens less than half the time.