I think that is a perfectly normal and clever question to ask! I would not worry about the previous response- some people have no manners! Some agencies, I am sure, pay reimbursement costs for driving clients to appointments and that kind of thing if they are really out of the way.
Some agencies, on the other hand will appreciate it if you have a car so you can drive to appointments quickly (for instance home to home care) but they will usually not pay for mileage due to wanting to keep their costs down. If they are a private agency, on the other hand, they may well pay towards travel costs at the rate of £19 per hour if you are contracted to work with a particular client in a State of The Art residential home for wealthy customers( these tend to be on the outskirts of London in places like Chalfont-St-Giles. I hope I have helped!.