Yes, you can do that using get_iplayer which is a free command line programme. The command line for downloading a TV programme is like this: get_iplayer --type=tv --pid=b0b052kc --modes=best

You need the pid code for the programme which appears within the url address box at the top of the screen. So for the Queen's Birthday Party on BBC One this evening, the url is http://www.bbc.co.uk/programmes/b0b0y1dg and the pid code is b0b0y1dg.

This will save a DRM free file to the default folder on the desktop called "iplayer recordings".

What was the programme called? I'll see if I can get it.