Best One Week Split
A practical first UK route is four nights in London, two nights in Edinburgh, and one countryside day or overnight around the Cotswolds if transport works. This gives the trip museums, theater, royal sights, old-town atmosphere, and village scenery without turning every day into a transfer.
London First
London can fill a week alone, so choose priorities early. Use one day for Westminster and South Bank, one for museums or markets, one for neighborhoods, and one flexible day for theater, shopping, or a short excursion.
Edinburgh Contrast
Edinburgh adds a very different mood: castle views, old lanes, whisky bars, literary history, and a compact center. The train from London is scenic but long, so compare flight versus rail based on your hotel locations and luggage.
Cotswolds Reality
The Cotswolds are beautiful but not always simple without a car. Pick a small number of villages, check bus or tour options, and avoid trying to see every postcard stop in one day.