Legally, as an employer, you will be responsible for salary, holiday pay, sickness pay and cover, insurance, NI, Tax Police Checks etc. You cannot have someone working 24/7 without them having time off so you will need someone to job share. You will have to itemise the job duties, will the carer be responsible for laundry for example?
These are just some of the duties of an employer. It might be easier to go through an agency, although probably dearer. That way they can provide cover for sickness and unforseen absences.
One other thing is that your Mum has to be prepared to share her home with a stranger. My late Mum would have preferred to have someone at home with her,( preferably me most days) except for the fact that she did not want to have a stranger giving her orders in her own home.
Good Luck.