Hi Ed
As Danny mentions, we have a Virgin Tevo box and can record 3 programmes on any station at any one time.....that is, programmes that are LIVE and being shown now......if you watch any of your recorded stuff on MY SHOWS you can still record the 3 live programmes at the same time...Catch up and BBC iplayer, ITV hub, 4OD, 5 etc can be watched while all 3 recording too...and you can watch any of your 3 choices as your recording them too....
Best way to find out what's available would include going to specialist TV Audio Visual shops such as Richer Sounds or Curry's......ask a specialist what's currently available.....
Good luck, Ed :-)