In Southampton, the going rate is £12 an hour, but every single good cleaner is full to the brim and turning people down. That suggests to me that good cleaners are too cheap. I tested it when a friend of ours who cleans (£12 an hour) had a customer die. A custy of mine was looking so I told her of availability of our friend at £16 an hour (my call not our friend's).
"Is she good?" was the question.
"Yes, excellent".
"Bit more than I used to pay but that's fine with me - get her to call me"
Happy customer, happy friend.
So, the usual lesson, do not underprice.
Vin