Trains:
This page links to live departure boards for buses and trains.
You will need to know the location codes.
For trains these can be found here: http://www.nationalrail.co.uk/stations_destinations/48541.aspx
For buses these can be found here: https://fusiontables.google.com/data?docid=15n7Rpi190vjrPcmbiT_hRcZ9JbXE8a_I1euHyg#rows:id=1
Data: Rail departure boards use www.nationalrail.co.uk's Darwin API.
Bus stop boards use TransportAPI.com