This is important for not only Whovians (Doctor Who fans) but would also be extremely beneficial for the BBC.
I believe that this would be an extremely profitable idea for them to do, and Whovians all over the world - not just the UK - would greatly appreciate it so much.
I for one, can't stand missing an episode or something when watching a series, which is why I was so irked to find that there were missing episodes in the old Doctor Who series...
This could be done in a number of different ways... It could actually be refilmed, but this may take a while to do...
You could also make animated recronstructions, that would be an easier example I believe, and you would only need voice impersinators, rather than look a likes, and just place them inbetween the episodes that still exist.
I think that I speak for all Whovians and the BBC itself, that this would be a widely popular and profitable idea.