Princess Elizabeth (now Queen Elizabeth II) married Prince Philip at Westminster Abbey in 1947, and they headed to Broadlands House in Hampshire for a few days for a romantic hunting trip (to each their own). Then up north to Birkhall, a part of the Balmoral Estate, one of the queen's favorite places for more hunting. After that, they boarded the Royal Yacht Britannia and headed to Malta, where the prince was stationed with the Royal Navy.
You may not be able to directly follow in the monarch's footsteps for this one (not having a private yacht or access to the stately private homes), but you can get some country luxury and pretend your royalty at the Four Seasons Hampshire, a restored Georgian manor house, which just opened a new Royal Suite. It's only (only!) £5,500 a night.
Or there's always the private cottages on the Balmoral estate, available for a week at a time.