I find it strange that rumors are circulating within the Forsyte family that Irene has been asking for a separate room. Soames doesn't seem to be the sort who would share such information, even (or especially?) with his father. It doesn't seem likely that Irene would talk about this to anyone, either. I have three guesses:

1) Irene told June, and June has told others. This seems unlikely to me, though, as it says that June is too full of her own affairs to pay attention to what Irene is going through.

2) The servants of Irene and Soames overheard this bit of information, and are in communication with the servants of the other Forsytes, who in turn inform their employers (thinking of Gosford Park ~ that scene where Maggie Smith's character is asking her maid for all the news from downstairs). This seems most likely to me.