I've only been there a few times on business, and only in London itself, but I enjoyed walking both sides of the Thames between Big Ben and the London Bridge (Tower of London area). I used a tripod and nobody seemed to mind. Trafalgar Square also had a lot of photographic potential.

For the countryside, I can't advise except to suggest that you try to find a copy of the British photo magazine Practical Photography (Barnes and Noble, Borders), it's usually about half landscape in content and British-centric for locations.

Take Care,