In reply to Alan M:
I have used a firebox on various Lakes sites, including NT ones, so wouldn't have thought a woodstove inside was viewed any differently.
I know for sure of several people using Frontier stoves in tents at Waterside Farm on Ullswater, though this was an organised event.
Here's a list of sites allowing fires, no idea of its accuracy. Scroll down to North West region, its in a funny order.
http://www.ukcampsite.co.uk/articles/view.asp?id=4
And obviously, its possible they'll see woodburners inside tents as more of a risk than fires outside, but I doubt it.