Plane tickets aren't that expensive (I see about 550 USD New York / London round-trip on Virgin Atlantic, and that's just the first search I did). If your trip is city-focused, you'd probably save a substantial portion of that on car rental.

And why does a cross-atlantic vacation have to be "luxury"? Most of the appeal of going such a long way is experiencing a different culture. Most of what you're buying with a luxury hotel is a more expensive lobby with more expensive services. (E.g. internet access cost is usually inversely correlated with room rate.) All you really need is somewhere safe, quiet and conveniently located to sleep, as you'll spend most of the day out of the room.

EDIT: I did another search, except in March instead of May, and I was seeing round-trip prices of 377 USD.