Remember it won't be a 37.5 hour week.
At least 2 hours a day will be travelling time for most cleaners and they won't be paid for any breaks (you expect them to eat right?) So at best, let's put it at 6 hours a day. Assuming they're full with contracts. So that's 30 hours a week. Sure nobody pays you for your commute but then you're not commuting three times a day at least. And there are the costs of all that travel.
Then remember they also will do all of their own admin, invoicing, chasing debt, procurement of chemicals and materials. Let's be generous and put that at 2 hours a week. Honestly as I work for myself it's likely to be more but let's give it the benefit of the doubt. So down to 28 hours.
Then as you say, no sick pay, no holiday pay (and also no pension contributions but let's ignore that for now). Let's assume 1 week of the year in total (i.e. 5 days) too sick to work. Let's hope our cleaner never gets seriously ill. So 7 weeks deducted for holidays and sickness.
28 hours x £22 x 45 weeks = £27,720
But remember a permanent job would be paid at the pay whether on holiday or not and through travelling times if you worked in a multi site job (as I have several times in the past) so the equivalent pay if this was a directly employed job taking account of that, paid breaks, paid holiday would be:
£27,720 / (52*37.5) = £14.22 an hour. Not including all of the other costs for working for yourself.
If you think that's marvellous for a job I'd argue is skilled, then crack on.