You might expect them to visit on 3 different days (to allow adhesive to dry etc), but to say it's a 3 day job is lunacy!
I don't see how anyone can really say unless they have seen exactly what is involved. Whats on the walls now, do they require stripping,sealing. How much cutting, how many trims. Is there a window reveal. Tiler to supply adhesive, grout, trims. Expensive labour rates near London. i probably would get a third quote though as there is such a difference.
Also the 20% VAT to consider and I think that you are looking at the higher end as I said, good luck with it anyway.
we got this done recently for a similar size area ended up paying £350. Got 3 qoutes between £200 and £575. £200 seemed too cheap, £575 is crazy. if you have the time this is doable in a day with a tile cutter and can be relivetively simply job.
Questions like this come down to a multiple of how long it takes and how difficult/skilled it is. Tiling is fairly easy (my mother taught herself it in a weekend when she was bored, because quotes were too steep) and reportedly this would only take a day or two. If it took two full days £500 would be reasonable. If it only takes a day (8 hours) of actual hands-on time, £300 seems more realistic. The really important question to spring on workmen is "how much are you charging per hour in that?" If they can't answer it on the spot, they're charging what they think you'll pay, not what they think their time is worth, and are to be avoided (unless you can successfully haggle them down to what you think the job is worth).
Don't tile over drywall. You will regret that. The least bit or house shifting or moisture leak will have tiles falling on you. -Hell, getting too frisky in there could bring them down. You want Hardy backer with a moisture barrier behind it in the best-case scenario.
...please excuse me for having never done any DIY before in my life (I have built 4 PCs, do they count as man points?!) what's drywall and hardy backer and moisture barrier etc?!