Hi Jo,
In principle it's a good idea, lots of girls do it, myself included.
There's no reason to think that the hotel will cotton on to you. The hotels are exceptionally busy
and if you pick the right one, very large, so unless you have an orderly queue forming outside your
door you'll be fine.
( please feel free to email me re hotels )
Just be aware :
A) It's saturated with WGs so a London tour requires a hell of a lot of advertising and hard work beforehand.
B) There have been a number of robberies and assaults there, so for goodness sake take the time to read
all of the warning boards and make sure you do your security checks.