London in the middle of the night

Hello all,
our trip to London in March will end with a flight leaving at 6:30 from Gatwick.
So we have to leave London at about 3:30 and won’t book a hotel for this last night.

Are there any suggestions, what to do in this last night (Saturday to Sunday)?
Are there any museums, shopping centers etc. open?

And: Are there usually lockers at the bigger train stations, like Kings Cross or Victoria?

Hi - there’s luggage storage at victoria

some galleries do late shows, but would close at 10, or 11 latest.

even gigs would finish by midnight, so unless you go to a nightclub you might be at a bit of a loose end for a few hours.

the airport shops will be the only ones open 24hrs…

or there are late movies, and some cinemas do all-nighters too:

and this place is always open