The whole "You need a new telly for Digital" is the pretty standard TV salesman con. You don't.
What you DO need, is a digibox of some description (Cable, Sky or Freeview) PER TV you want to watch independant channels on. Similarly if you have a VCR you will need a second box for it if you want to record one program and watch something else (this is why Sky+ exists).
If any TV salesman says you need a new telly for digital, tell him to f*** off
