I've seen the 'magic number' quoted at 250hrs/year (below which it is cheaper to hire)
Rules of thumb are subject to too many variables to be reliable in all cases ... that said, I have often seen references to 100 hrs per year (as ChampChump indicated), but never 250.
Possibly things might be different in a high cost environment like the UK; but both renting and owning would be more expensive, so I don't see why the 100 hour formula wouldn't work there as well.
Anyway, in most cases it is probably irrelevant whether the number is 100 or 250, or any other figure. The average recreational pilot probably flies perhaps 30-50 hours each year (new owners often fly much more in the first year or two of ownership, but then taper off as the novelty diminishes); and renting will always be cheaper for that amount of usage.
I'm inclined to think that ownership very, very rarely makes sense from a purely economic standpoint ... but there are usually other, less tangible, benefits that may outweigh the added costs.
Owning a syndicate share can allow one to enjoy the best of both worlds; although if things go badly, partnership can raise all kinds of unique and unpleasant headaches.
The 'bottom line' (IMHO): there are pros and cons to all methods of gaining access to private flying, and compromises are inevitable for all but the extremely wealthy.
P.S. Thanks to strake for sharing his experience.