My DS applied for Falmouth but didn't apply on day one (as he hadn't accepted his offer by then). He couldn't apply for any of the room types he wanted as they were vastly over subscribed, and so didn't appear on the form, by the time he applied: so there were only shared rooms on campus, shared rooms 10 miles away or bunk rooms on campus.
We discovered that all the single rooms, whether on or off campus, had gone within the first few hours, (and the website had crashed) but that is unusual I believe, due to Falmouth rapidly expanding and not having sufficient accommodation to offer single rooms to all who wanted them (something we didn't know as it had not been made clear when we looked round).
He has a firm place (applied after A levels) so is definitely going there. He has now been allocated a shared room on campus - the location he wanted but not the shared room. We have paid a deposit and are hoping that once he gets there, single rooms may become available and he can switch if the shared room doesn't work out for him.
My DD applied to York as soon as it opened, but we don't get to hear until results day which of her choices she has got (apparently she applied for all 9 choices in order of preference, just in case...!)
Not sure I am being very reassuring here, but I would say apply earlier rather than later.