I think that moving your child to a small, nurturing private school would be wonderful for your daughter if you can afford it.
A word of warning about bursaries, though. In general, these are few and far between, and mostly offered to scholarship holders (or rather, they start at the top, and by the time they've got through the scholarship holders, the funds have run out). At my children's school (which is a fairly average fee paying school, not a pushy results factory, nor a big name) in order to get a scholarship at 11+, and therefore in with a shot of a bursary you would need; for sport, playing at least one preferably 2 sports at County level, for a music scholarship two instruments or more at grade 5 plus, for an academic scholarship, exceptional performance in the entrance exam, plus excellent performance at interview. Bursaries just aren't available for being bright, or for having some musical ability or for being fast/strong in sports, they are awarded to the very , very few students who stand out head and shoulders above all the other bright, talented students.
That said, regardless of what happens at secondary age, it sounds as though it would be a good solution for the next 2 years, and in the scheme of things £20k on the mortgage is not that big a deal.