If your week is London, Bath, York, Manchester, Liverpool, Edinburgh, Glasgow or Cardiff, plan rail first. Hire a car only on the days the destination stops being a walk from the station.
When the train wins
City-centre to city-centre, no airport security, no Congestion Charge. Match the London terminus to the hotel. Use UK rail travel and the hub route directory.
When the car wins
Beyond Inverness, the Causeway Coast from Belfast, Swansea-to-Gower afternoons, and rural nights the bus would swallow. Pick the car up where driving starts — see car hire.
Hybrid weeks
Rail to Edinburgh, then a Highland hire for two days. Or rail to Belfast city, car only for the coast. Do not collect a hire car at Heathrow on day one for a London sightseeing stretch.