How long for?
Where are you setting off from? (If you live in Cambridge or Orkney isles much of your budget would go on travelling if we chose west coast of Ireland, for example
North Wales for scenery. Highlands of Scotland very nice. Southern Ireland I’ve heard is good. Also Hereford very pretty. A road trip around UK avoiding motorways.
Head east and when you come to the sea turn left. Then go all the way up the east coast, stopping wherever and whenever you like, until you get to Edinburgh. I've done it and it is stunning.