Yes. If you are an hourly-paid worker and your contract terms require you to be in attendance at a service user's home – so that, for example, failing to do the overnight shift, or leaving the premises during the night without permission from your employer, could lead to disciplinary action – you are entitled to at least the National Minimum Wage for the whole shift.
The fact that you are sleeping is irrelevant to the question of whether or not you should be paid. Likewise, it makes no difference whether or not a service user actually wakes you up to ask for help during the night.
You are entitled to be paid because by being at the premises at the disposal of the employer, you are 'working' for the purposes of the National Minimum Wage regulations.