I’ve done loads of solo road trips. Most of my riding mates are married and can’t get time off so I generally head to Wales/Lakes/scotland for a couple of weeks just loading the car with bikes/tent/boots etc. I find I’m much more lonely when I’m in big towns with lots of people I don’t know then when I’m the only person around for miles. I’m pretty happy with my own company though, so maybe try a weekend and see how you get on.
For bottom half of UK, then Dorset is great (Isle of Purbeck is fab), or Somerset/Devon? I spent a very happy week camping in the Camping and Caravan Club site in Porlock a couple of years ago. Great scenery, great riding (as long as you don’t mind some pretty steep climbs), and you are by the sea as well. For that one a couple of mates joined me for the weekend for 2 days riding in the Quantocks which was superb.
Shropshire is great as well, especially around the Long Mynd and there is lots of nice riding around the Welsh border and mid Wales which tends to be very quiet.
Have fun!
Boris