How much tolerance do overhead AC and 3rd rail DC have for reduced voltage? I'd assume that for both, especially 3rd rail all trains would have to run slower and maybe turn down things like air con
Last time I spoke to someone I remember 18.5kV being mentioned as a lower limit, but it would mean disabling and overriding the tap changers at the feeder stations that are designed to try and keep it at 25kV. A significant amount of these tap changers are local control only and would be very difficult to change. You would probably also find that the more modern stock will still draw the same power regardless, so you would (if anything) want to increase or keep the voltage as close as possible to 25kV to minimize grid losses.
The same holds true for the 3rd rail network, the modern (ac tractioned) units and to a certain degree RPA controlled DC stock (455s in their old guise, older LU stock etc. They will continue to draw a similar level of power until a threshold voltage is reached when they will begin to load-shed regardless of line voltage.
All modern transformer rectifiers have tap change regulators that will keep the voltage as close as possible to the required line voltage on the DC side, usually ignoring the effects of transformer and rectifier regulation (in the true sense of the word).
As a bit of background, T/R sets are usually fed at 6.6kV, 11kV or 22kV and incorporate several secondary windings in order to feed a 12 or 24 pulse rectifier (or sometimes a pseudo 24 pulse rectifier).
Further background, the rail sector's energy consumption for traction pales into insignificance compared with a significant amount of industry, who's supplies are individually switched by the DNO (sometimes even National Grid) at an HV level, usually on their own Tx. Industry cooperation will be being sought for them to shut down when the grid needs some extra juice.