First of all, Hymie, thanks for your kind comment about me on that boiler thread the other day.
As soon as "London" is mentioned, all bets are off. I would certainly expect to see £200 per day charged.
I would guess he's going to make more than that on the bathroom. I can't see a small bathroom taking a week... even one guy on his own........ unless it's not just a straight substitution. But ... if a fair bit of tiling is included, then there's a day and a half's work in itself.
In short, if it's a simple refit... just connections to existing hot, cold, and waste, I think you could shave 2 or 3 hundred off that.
The kitchen rather depends on how much fiddling about it entails. Assembling and fitting carcases takes no time. Worktops would take only a few hours. The time goes in all the cornices/plinths/ pelmets /trim etc etc.
Having said all that, I'm fitting one for a friend next week. Slightly bigger than your kitchen, for around £1600 , including simple tiling, sink plumbing, and moving a couple of sockets.
Your big problem around London is that there's always someone around who'll do it cheaper, often with disastrous results. I do think those prices are on the high side, but, I would be wary of going too cheap unless you have the ultimate faith in the guy doing it.
What I'd really like to know is... why you're not doing it yourself. From what I've spoken to you about on this site in the past, I'd say you were more than capable :o)