ADDENDUM - I had a nice conversation with Joe Lidster on Twitter about this story, and this is the upshot of what he said when I mentioned the similarities with Rose in Aliens of London - so although he wasn't necessarily inspired by it, it's a story he holds in high regard:
"I’ve just checked and it looks like I was writing it towards the end of 2005 so I’d have seen it happen on TV. But I think I’d started writing it as an attempt at a Missing Adventure long before I did anything for Big Finish. I’d always thought that it was odd Peri never went home etc considering her family set-up is very clearly defined in Planet of Fire. But yeah, obviously there are similarities with the TV series but Aliens of London is still my fave Dr Who of all time :) ... In fact I remember I started writing it in 2001 because I was on a train and that had given me the idea - for some bizarre reason!"