So just googling about it seems there's no official API for TFL. One guy has made a public beta for the line status which seems to be working. Basically he scapes the TFL website once a minute and makes the results available for query.

tubeupdate.com

National Rail have a very nice API for train (not tube) depature boards.

livedepartureboards.co.uk

Would be great if TFL would get their act together and produce an API for the same for the tube and the buses.

Other things you could do is to parse the live depature boards from here (to be honest even opening this in a browser window would be a great start :

TFL Live Depature Boards

Finally - a lot of thjis info I got from this site here which may be useful to you - scroll down to the travel section:

RewiredState

Hope this helps because a decent london transport app would be fantastic for me.