I live close enough to London to be caught in its vortex, but far enough out that it takes me a couple of hours to commute in. I get the emails from recruiters about positions. Some of them have even actually read my CV and informed me of jobs that I could do. "Remote working for some/most/all of the time?" I ask. "No, you have to be on site," I am told, over and over again.
I can (and have) worked remotely and, if anything, I've been more efficient. My home office is set up the way I want it so I'm comfortable and less distracted. If someone really, really, *really* needs me they can call, but other than that it's email or some other messaging service, things that I can turn off if I need to focus on a problem. It's difficult to turn off your co-workers in an open plan office. (And, as an aside, if there's anyone in a position of political power reading this, please put forward a motion banning people from installing Sonos speakers in the office!)
Widen your talent pool, trust the people that you hire, but don't screw them over by offering peanuts just because they don't have to pay London prices.