I passed through 3 closed Underground stations on the same day.

Warren Street (Victoria Line) - we stopped momentarily which I guess is to
do with ATO (doors did not open). Not sure about tape.
Wimbledon Park - passed without apparent slowing. Tape all round the
platform.
Notting Hill (Circle) - passed at a fast jog. Tape all round the platform.

Which set me wondering. What are the rules for passing through stations
where work is in progress?

And to expand slightly beyond LUL with Glastonbury approaching I know they
put a speed limit on trains passing through Castle Cary (20 mph I believe)
so do the same rules apply where large crowds are expected?