Yes. This is working time for which you should be paid.
Your schedule is under your employer’s control, and it’s not as if you can go off and decide to do something else with your time, instead of travelling to your next appointment.
In fact it's likely that your employer is keeping a close eye on your schedule, to make sure you are where you are expected to be. If you are not sure of the position, ask your union rep.
Your average hourly rate, once these hours spent travelling are added to your working time, must be at least the National Minimum Wage for your age.
If you are not yet a union member, browse our Union Finder tool to find the union best suited to your needs.