Georgian top floor flat, sounds very nice- Would it happen to be a listed building?
£11k is OTT for a standard 2000 sq ft house, I would have guessed at £5-6k labour + £2k materials (absolute tops).
If the property is listed, if the work includes re-plastering and decoration then just maybe it would stretch towards the £10k mark.
Last full re-wire (absolutely everything) inc 12 final circuits, 17w split board, 57 double sockets, 17 light positions + TV, Voice, Cat 5 and even the door bell came in a £4.6k labour (me-billy no mates), £1.8k materials (MK).
That was on a 4 1/2 bed Edwardian semi with full repair, ready to decorate plastering finish. It was one of those jobs where everything was surface and everything became flush.
As mentioned get some more quotes and consider helping the quote process by offering:-
* Free, unfettered access to certain areas (such as clearing bedrooms of furniture and not occupying them for short periods
* Carpet man to re-fit / stretch carpets
* Planning the repair / redecoration of chased routes- who and when
Basically try to simplify the work and the man hours have to shrink, hopefully to a point that become a fair cost for work.