If you take on someone to work for you in your own home, such as a nanny, then you are likely to be their employer and will be required to deduct tax and NI contributions from their earnings under Pay As You Earn (PAYE).
The employment status of a worker is not a matter of personal choice and even if your nanny were to agree to set up in business as self-employed, then this does not automatically exonerate you from any potential PAYE liabilities or other employer’s obligations.
In most cases it will be easy to decide if someone is your employee as you will have advertised for the position and they are likely to work only for you, under your personal control and direction, for hours and pay specified by you.
In contrast, if you were to buy the services of a nanny from a business that has several employees and clients or through an agency, then that business or agency will be the employer and not you and they will be responsible for all employment rights and the operation of PAYE.
So if you want to avoid the tax responsibilities of employing a nanny get one through an agency.