On a 125, I’d get a decent map and start exploring the white roads with some minor A/B roads to link them up.
Look for ones that are nice and twisty with no, or few, villages and lots of open country on both sides.
Barnet, Potters Bar, Essendon, Bayford, Newgate, Northaw, Potters Bar, Home
Not far from you, Welwyn to Hertford A414 will let you max out a 33hp bike in relative safety and enough bends to be fairly interesting.
On a small bike, take a look at a large scale map. You’ll find that the A routes tend to divide the country up into cells. Within the cells you’ll find loads of minor B roads with much less traffic. Pick one or two and go off and explore. Just take a few random turns and see where you end up.
Take a long weekend or a week off some time in the summer and go on a long trip avoiding motorways. There are loads of good places to go in the UK, all the way out to the North of Scotland. It’s not hard to get a small tent, a sleeping bag and a change of clothes bungeed on the back of a bike. And if you pick your spot away from people, you can camp pretty much anywhere for a night without any bother. Just keep turning down smaller and smaller roads and look for a coppice or small wood.