Your average hourly rate, across your ‘pay reference period’, must be at least the National Minimum Wage. Your pay reference period is a month (unless you are paid weekly or daily, in which case it will be a week or a day).
Where you have no fixed place of work but instead you work from home visiting service users in the community, time spent travelling to your first and from your last appointment of the day is likely to be classed as 'working time'. As such, your average hourly rate must be at least the National Minimum Wage rate for your age, once these hours are added in.
The position is different if you have a fixed place of work that you attended every day, for example, if you work as an hourly-paid careworker in a residential care home. Then your time spent simply travelling to and from the residential care home at the start and end of your working day without performing any work duties would not be classed as 'working time' and you would not be entitled to be paid for it.