In the UK, all eligible workers are entitled to receive the National Living Wage (formerly National Minimum Wage) even if they are not paid by the hour. This means that if you are a live-in carer and you are paid by the day or by the week, you are still entitled to receive the National Living Wage and your equivalent hourly rate must be at least the National Living Wage.
If you are a self-employed live-in carer you are not eligible to receive the National Living Wage. Obviously this does not mean that you should be low paid! But it does mean that you would not ever be able to make a claim against your employer for non-payment of the National Living Wage (as you are self-employed).
As the nature of live-in care work is such that it is very hard to actually specify when you are truly working or when you are on a rest break, most employed live-in carers will have an “Average Working Hours” agreement with their employer. This basically means that you agree that on average you are working a set number of hours per day. This is important as it would be this average number of working hours that is used to calculate your equivalent hourly rate of pay. So for example if you are paid £560 per week, and your average working hours agreement is for 8 hours per day, then your equivalent hourly rate is £10 per hour.
Of course whether you are actually working the “Average Working Hours” is important. If you feel that you are working more than this then you should make detailed notes and raise this with your employer.
The government website has more information on the National Minimum and Living Wage, https://www.gov.uk/national-minimum-wage