Depends on the exact definition of demand responsive bus services.
Most areas have a dial a ride organisation where people can book a journey 24 hours in advance and then a route is drawn up to cater for the bookings with the minimum number of vehicles and mileage.
It may not be quite what you are after as it tends to cater for people who cannot use mainstream transport because of age or infirmity. However the Community Transport Associaton may be able to help.
http://www.ctauk.org/