To add to Ethel's excellent answer:
Freesat from Sky simply requires you to buy a card, for a one-off payment of �20, and insert it into your existing box. You get a subset of the subscription channels. (See Ethel's link for details). HD channels aren't available through Freesat from Sky. (You have to get a Sky HD box and take up an HD subscription to receive the service. That applies even if you only want the 'free' HD channels, such as the BBC service).
The BBC/ITV system offers a smaller range of channels. It requires a separate box but you
might be able to use the same dish. (It's a case of 'ask in store for details'). When purchasing a box you can choose between a 'standard' or 'HD' version. If you get an HD box, you'll be able to receive 'subscription free' HD services (such as the one already in operation from the BBC and the new ITV service which will start shortly).
To back up Ethel's second link, here's the official website for the BBC/ITV service:
http://www.freesat.co.uk/
Chris