I may be entirely wrong, but I think they only have the trailers for resting when they're actually on/around the set and not filming. They live in flats that the BBC provides, IIRC. There was a bit on Charlotte Church's show interviewing Billie Piper that talked about that, as well.

Also, I'm not sure what year your fic is set in, but David's mother died in July 2007. That's about "my parents would disapprove" bit.

In case I didn't say this loudly enough, I loved the story (I blame versaphile for corrupting me with her lovely RPS). This is just random nitpicking.