I would have read this book in the early 80s. It's probably just about SF as it involves tech that certainly wasn't available at the time.
An American teenager moves to London; his father somehow has a job at the Tower of London so they live in housing there, making friends with other kids whose parents are Yeoman Warders (I remember them being very insistent that they didn't use the term Beefeaters).
Ghosts of historical figures like Anne Boleyn start appearing on the battlements. The boy and his friends work out that they are actually holograms being projected from the top of the Post Office Tower (as it was then).
He quickly gets involved in a complicated plot involving a new European currency called (I think) Europounds; there's a slightly deranged economist who wants to destroy the currency for some reason. The climax involves the money being transported in a white truck being guarded by a black car, and duplicates of both the truck and car being switched (so that the real truck ends up with the fake car, and vice versa).
Other points I remember:
They go to the revolving restaurant at the top of the PO Tower and sneak downstairs to search for the projector, when the boy goes back to their table he initially can't find it because it has revolved.
While investigating the currency plot he breaks into an office building and sets off the sprinklers with a lighter.
At one point the accidentally break a bit of the masonry in the Tower of London and find a pottery sherd with "OLWORT" inscribed in it; they think it's probably very old until someone points out that the full word was actually "WOOLWORTHS".
