With out knowing any more I can say that £800 sounds a little low with tiler supplying everything except tiles. Also, the high quote may be a result of everyone being very busy. The best thing is to get more quotes - will give you an idea on current prices. And ask about availabilty. Not so much of a problem if you are booking months ahead.
And any one planning work should be booking months ahead.
We get calls from people who tell us they've bought and got all their new bathroom stuff can we fit it as if we'd be available within a few weeks! We are amazed by these calls as we are typically booked up 4 months in advance and so is everyone else we know.
PigletJohn - the floors's in 2 parts if this helps. 1 new concrete in new extension; other half old kitchen with suspended timber flooring. Our builder will have hard boarded it in advance of the tiling.