There's more to the UK than London. Its a whole continent in microcosm: The Lake District; the coastal cliffs and marshes; The Peak District and the Yorkshire Moors and Dales, as well as a wide range of towns and cities, all built in local vernacular styles and materials. Don't stick to the obvious, try cities such as Newcastle upon Tyne as well as Durham or Glasgow as well as Edinburgh.
And by the way - post 9/11 the police are not quite so accommodating!!!