I am central London and would expect to pay around £350 for a prof clean for a three bed house to include oven, carpet steam clean, insides of cupboards, and the outside of windows, in an empty property which is reasonably clean to start with. Essentially two people working efficiently for a full day. So probably around £15 per hour once parking and travel time are taken into account.
It could be more if the property is occupied and grubby (like mine!) but they normally come round and quote. There is a real difference between domestic clean and prof clean.
It will be less outside London, though my experience there is that there, cleaners tend to be less "professional". More normally a couple of school run mums who have a gig of doing one off cleans for the local letting agent. So not the same whirlwind and thus about the same cost.
(Be very wary of people who advertise on the internet. Prof cleans are a real cowboy industry. One very high earning tenant - probably around £half mill pa - tried to argue against using my preferred cleaner on the basis he had found someone for a third the price. I broke costs down and suggested the only way the firm could break even was by paying staff about £2.50 an hour. The tenant could not see a problem in that!)
The good thing with your job is that you could schedule it at the cleaners convenience, which should bring the quote down a bit.
And if you are in central London (and why would you not be....as I plan another foray to the property board to argue the case for London living) my cleaner is fab. And could dig out a couple of suggestions for Dorset as well.