The 'unofficial' word from someone who works on the underground...
"You need a permit to photograph or film on the Underground, trains are a big no-no without permission. Depends on what type of photography you want to do tbh.
Ordinary for your own purposes you'll be fine just taking a camera around with you, but you're not allowed to use a flash anywhere unless you have specific permission. Deffo no flash on the platforms. With this type of photography you can usually get away with just going around on your own, but if its a specific station you want to photograph then just knocking on the Supervisors door and letting him/her know you're there is curteous, though again you might get a jobsworth insisting you have a permit.
Commercial photography has to have an official permit/licence.
The above applies to filming aswell.
Tripods are another big no-no as they are considered a safety hazard.
hope that helps."