Henry VIII's bath, one of the few parts of his Palace of Whitehall that survived the Great Fire of London in 1666, is almost impossible to visit, as it is the basement of No 10 Downing Street. The closest accessible Tudor bath is the "Roman Bath" on Surrey Street, formerly part of Arundel House. (Insert jokes about dirty politics here).
But the fabulous thing about living in a city with so much history is that one is always discovering something new. This blog post has fabulous photos of the Cardinal Worsley's York Place wine cellars, which were incorporated into Henry's Palace.
The Last Places
They are in the basement of the Ministry of Defense, so still hard to access - but not as hard as getting an invitation from the PM to poke around his basement ...