Dont forget that airports often ended up on floodplain as the original developers (often the MoD) had to find flat land to easially build airfields on - where do you find large areas of open flat land with no existing developments? Floodplains....
And as has been said. At LGW the floodwater got into the substation making it dangerous and requiring shutdown. Firing up generators would supply power to the airport ring which would energise the airport side of the substation, which is flooded, and dangerous to be energised....
However, LGW had contingency plans for this which they used, they moved North Terminal Flights to South terminal where possible - it created delays, which are to be expected when yoh are operationing on contingency procedures rather than your primary procedures, but the flights still operated. Only BA did not temporarily move to South Terminal, instead staying in the North Terminal for whatever reason.
Certainly where I work our power loss contingencies (I.e. the generators) supply power to the essential systems (via a UPS) and a small amount to non essential systems (such as only 1/3 - 1/4 of terminal lighting, enough to get by but not the normal level, flight info screens shutdown, advertising displays turn off. Just enough systems to remain safe, not enough for the customer service desires.