simonhill wrote:When people ask such questions, I usually say what do you want to see and what interests you?
A bit of research to find places that appeal can often lead to a route naturally following on. The UK is a fantastically diverse country in terms of scenery, topography and culture but not all of it may appeal to you. Stonehenge or Stratford upon Avon, Constable Country or Wordsworth's Lake District. We can recommend until the cows come home, but only you know what you like.
It would also help if you said what sort of accommodation and what budget. This could be another deciding factor. Camping, hostels, b&bs, or hotels. Not forgetting warm showers.
I'm not trying to be awkward, just trying to help you pin things down a bit.
...............and finally, no one has answered about hiring a decent bike. I imagine there are places, but I have no idea where, or how much. My normal recommendation is to bring your own.
One of the reasons I suggested he use Google street view to check out a route. I find it invaluable. What is sometimes called a cycle path turns out to be a mountain bike cycle path.