Jeremy, many organisations that employ carers do not regard the time spent getting from one client to another to be payable time. The result is that they will usually pay you towards getting to your first client, and home from your last, but nothing for the trips in between. All three of my womenfolk have done this kind of work in the past, and they would usually have between 6 and 9 calls a day. I know of others who have more than that.
You are fortunate because you have a 'normal daily commute', suggesting that you have a base office. Expenses for travel away from that base office is covered by existing legislation. What I have described above is not.