Lots of assumptions going on. Firstly, because the cleaner says she doesn't pay tax, this doesn't mean she is 'dodging' it, it is more likely that she doesn't earn enough. Secondly, she is allowed, in fact encouraged, to work while claiming top up benefits, it isn't the case where you work or don't work. Thirdly, very few people with a family are able to work on minimum wage (let alone below it) without getting some sort of top up. Fourthly, the person who said that £12 an hour was more than she was paid as a manager; you were on an annual salary, the cleaner isn't, she only gets paid for working, not for traveling, no holidays, no sick pay. She is unlikely to be working more than 4 or 5 hours a day if she has school age children. I used to own a cleaning company, my staff were all employed, got 5.5 weeks paid holiday, sick pay, maternity pay, and travel expenses, they were insured as were the clients' homes and I can assure you that even leaving out the overheads and my small salary, everyone should be paying around £12.50 an hour minimum. If you are unhappy about the potential for 'benefit fraud' then pay direct to the cleaner's bank account.
The King is to resume some duties.