The BBC's average weekly reach is so high that it's unlikely that many of the people who claim never to watch any of their channels, really, truly never watch any of their channels.
In any case, we already have forewarning of some of the budget cutting as it has been drip-fed into the media over the last few weeks. The axing of Doctor Who Confidential has the Who-nutters up in arms as you would expect. Tomorrow the BBC will also reduce the number of red button streams it broadcasts via satellite, allowing to drop from 7 transponders to 6. That should save a pretty penny as well.
Once relocation costs are paid down, the closure of Television Centre and the basing of certain departments in Manchester instead of overcrowded, overpriced London should also bring some savings.