Its true you are not her employer and as long as she is registered as self employed with the IR then she is legal to hire whether you pay in cash or otherwise. Does she do receipts - you could ask she will not wish to if she is illegal.
If not then it not legal and YOU could be classed as her employer if the IR got wind of it and then you would be liable to back pay all the tax you should have been submitting as her employer (even though you were not aware that she wasnt registered) You really do need to make sure people are in business legally or it can come back on you fair or not.
Although as a sole trader (if she is) she is not legally obliged to get public liability insurance for herself but DO NOT hire someone who isnt covered. If they were to wreck your expensive items or burn your house down or cause a flood she would not be covered, also if she or any staff she may hire should have an accident on your property you need it to be HER liability not YOURS.
I am in the industry and these two things are key if you hire an individual - make sure they are registered to pay tax and fully insured and then you are safe from liability in any direction.
Obviously check her refs to make sure she is honest too.
I have a cleaning service and will only hire a tiny percent of people since it is such a personal service to be performed in a client's homes. Trust is a HUGE issue - I will not give client's house keys out to just anyone, you should give your house keys just anyone either - check everything, refs, insurance documents, personally I wouldn't pay cash just in case she isnt legal, if she's an above-board service she wont mind if you do BACS transfer or something to pay.
When I was starting out in business I discouraged cash payments as I thought it unprofessional and thought would give the wrong impression but some wanted to pay that way - that's fine too as long as its their preference and not the cleaners.