In one of my preference surveys (1988), 81% of my British respondents said ‘yes’. They are the people who prefer ruːm, with the GOOSE vowel. The remaining 19%, the ones who said ‘no’, prefer rʊm, with FOOT. The 81% must also include the people from Scotland and Ulster who have no GOOSE-FOOT contrast, just an undifferentiated u or ʉ vowel.
Yuko Shitara-Matsuo’s 1993 survey of AmE preferences showed an even larger majority, 93%, for the GOOSE vowel.
A few days ago Stevie Rickard wrote
I'm teaching 1920s RP to some actors and I've advised them to pronounce 'room' rʊm on the basis of almost nothing at all. Shame on me. One of the actors thinks he was told to use ru:m for the same accent in another play. Would one of these pronunciations have been more acceptable than the other in this accent 90 years ago, do you think?
Fortunately I can quite easily answer this question. In the 1956 edition of EPD (and perhaps earlier — I haven’t checked), Daniel Jones, while still prioritizing the FOOT vowel on this word, commented
Note.—The use of the variant ruːm appears to be much on the increase.This suggests that previously it had been unusual. I conclude that in the 1920s rʊm would have been the more usual pronunciation in RP.
Returning to the present day, the pronunciation of room as an independent word is not necessarily a guide to its pronunciation in compounds. Some who say ruːm for this word on its own nevertheless say rʊm in bedroom.
Personally, I’m with the minority who say rʊm in all environments.
We also get some fluctuation between GOOSE and FOOT in broom and groom. But as far as I know boom, doom, loom, and zoom always have uː. So does bloom, although in the old-fashioned mild BrE expletive blooming some use ʊ.