Re the Houses you showed phtos of--remember that the white house is not just a residence but an office building and a cermeonial building. As i recall, 10 Downing Street is just the residence of thePM, his office and most ceremonial functions are elsewhere, correct?
10 Downing Street is also an office building, where the Cabinet meets, etc. It is, of course, more spacious than its facade would suggest, but no more than to be purely functional.
No more than to be purely functional? i googled it and it appears 10 Downing St has over 100 rooms; pretty much like the White House with 132 rooms. I'd bet the staffs are similar (except for landscapers).
Scooter--I doubt there are many ballrooms; it seems to me that most large functions are run out iof the East Room (as are press conferences) which does not appear to be all that big, and I doubt there are any bigger. As for bedrooms suitable for royalty, I know there are a few bedrooms (like the one mentioned by Dales) but am not aware of royalty (or many others unrelated to the presidnet) staying in any of them (if I recall, there is a guest house for visiting foreign official somewhere in Washington (not on th White House grounds), but most stay in hotels or at their embassies/abassadorial residence). Like 10 Downing Street, the White House is mostly offices--the oval office is undoubted the largest, but probably the only big one. I've never seens a picture of the PM's office, so I can't compare it, but doesn't he have an office in the House of Parliament (WHitehall?) as well? The president has only the oval office.