It seems obvious to say that, with climate change, the potential for flash flooding, particularly from summer thunderstorms, will only increase, quite possibly dramatically. Urban stations are those might likely to be at risk, and those in London especially so, given that the average temperature at these will be higher by a matter of degrees than other cities and towns.
I grew up in London and my local station as a child, Clock House, was once several feet under water (as was our garden which backed onto the railway, with the water lapping against the top step to the back door). That was in the late 50s or early 60s, and no doubt the potential is there for far worse now.
How robust are the drainage systems at urban stations? Is it assumed that water will mostly just drain through the ballast?
Yes climate change is expected to increase the frequency and the severity of flooding, and increased flood risk should be taken into account for new or refurbished infrastructure.
The costs of major flood proofing throughout the network would be astronomical, but an incremental approach as part of other works should be considered.
Footbridges are better than subways for example.
Track side signalling equipment should be elevated on concrete plinths in high risk locations, and new installations should be elevated even in lower risk locations.
New bridges over rail lines should have extra clearance in order that the track may be later raised without altering the bridge.
Stations prone to flooding should have electrical equipment at high level.
London tends be to very warm due to the "urban heat island effect" but this does not increase the local flood risk. A warming climate increases evaporation from land and sea, and this extra moisture tends to fall as extra rain. The LOCAL temperature at the place where this extra rain falls is not relevant.
With the prevailing wind being from the west, much of the rain in the
UK▸ results from evaporation in the Atlantic, which is warmer than in the past.