The UK holds a wide range of experiences, and they do not all sit easily alongside each other in a single trip.
A few days in London is a different kind of travel to time in the Scottish Highlands or along the Cornish coast. The Cotswolds moves at a pace that is hard to appreciate if you are also trying to take in a city. Scotland has enough to fill a trip on its own.
Being clear about what you are actually looking for, whether that is landscape, history, cities, or coast, makes it much easier to build something that holds together.