Doesn't seem to matter where you are, so long as it's not inner-London where prices are very cheap (I am give to understand there's plentiful supply of labour, but that may not be true), prices can be between anything and anything.
£16ph is very cheap for anywhere, simply because the ball-park figure for working out the "extras" anyone on a payroll would get (e.g. holiday pay, NI contributions, etc.) is 30%, so add that to minimum wage of £12.21ph and it's coming out at around £15.70.
Now, it could be that your cleaner loves being self-employed as opposed to working for a company, but she really should be charging way more than she is, especially if she provides materials, and covers her travel time, travel costs, and time spent at home doing whatever is needed to keep her service running.
Have you got a Molly Maid near you? If so, it would be well worth getting an in-home quotation for your job (they only charge per-job and will never quote over the phone), to find out what their rate is, as they are well known for being the leader for paying staff legally and properly, and for charging accordingly. The actual quality of the cleaning will be generic, variable, and subjective, but they are "proper" and reliable.
From there, you can work out for yourself how much someone who actually wants to clean your house and who is offering you a bespoke service is worth to you.
HTH.