I am not a lawyer. This us just chat in a chat forum.
Apparently the law is that is a A does work B for money then if A is running a business, all B has to do is pay the money. National Insurance, insurance, income tax, and so on are the responsibility of A. So A could be a self-employed individual duly registered as such or a business that sends a human to do the work. If A is not either of those, then (except *) B is the employer with all of the obligations over National Insurance, insurance, income tax and so that that implies.
The * is that I read somewhere that there is possibly a special arrangement if the work is personal care as in washing of a human with a disability who arranges that for him or herself, but not for gardening, housework at all, nor for personal care if the arrangement is made for one human by someone else. But I don't know the details.
It is important to understand where financial liability rests if the cleaner has an accident while at work.
It may well cost more to do it through an agency so that all the person having the work done has to do is pay the money, but that is far better than ending up in court or paying a penalty notice to Her Majesty's Revenue and Customs or having o sell the house to pay compensation for an injury because as employer not having had the required insurance policy.