Not every car holds its wheels on with nuts. A lot of European makes use bolts instead, which thread straight into the hub with no stud behind them, and the locking one in the set behaves rather differently when it goes wrong. A seized nut has a stud to fight against. A seized bolt is turning in a threaded hole in the hub itself, so the damage from forcing it lands somewhere far more expensive. It is worth knowing which your car has before anybody starts levering at it.
Either way the answer is the same tool used with more patience than force. The extraction socket goes over the head, bites into the outside of it and comes back out slowly, and the replacement is matched for thread pitch and length so it seats properly. Around SE15 the car almost never has to move for this. It gets done on the street it is already parked on, off Bellenden or up towards Nunhead, because finding a second parking space here is a bigger job than the wheel nut ever was.
Salt is what does most of them in. Cars parked out on the road, on Peckham High Street included, get the worst of it. We do that where the car stands in SE15, then fit a standard or replacement nut so the next wheel-off is a normal job. Valve in Nunhead, balance in Bellenden, pressures before we go. The wheel comes off in Bellenden, not on a ramp in East Dulwich.

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Parking around Rye Lane is hard enough to find without giving a space up for a job that takes twenty minutes at the kerb. The extraction gear comes to the car, the fastener comes out without the hub or the alloy taking any of the load, and a matched plain one goes back in so nobody has this problem again.
An owner near Peckham Rye had bought a socket set for studs and found bolts threaded into the hub instead. Different tool, different technique, and forcing it would have been an expensive mistake.
A car that had changed hands twice on Queens Road came with no locking key at all. Four heads out, four plain ones in, done at the kerb in under an hour.
A driver was turned away because the bay had no extraction gear that fitted. The wheel came off on their own street instead, and the tyre change happened afterwards.
Look at the centre of the wheel. If there is a threaded stud poking through each hole, they are nuts. If the fastener disappears cleanly into the hub with nothing behind it, they are bolts.
It changes how much force is safe. With bolts the thread is in the hub, so a stripped one is a much bigger job, which is why they come out slowly rather than violently.
Yes, and that is where nearly all of them get done. The car keeps its space and the fitter works alongside it.
The thread pitch, the length and the seat type get matched to what came off. A fastener that is right in every way except length does not hold the wheel properly.
That is normal for the ones we are called to. The socket cuts into whatever is left of the outside, so a mangled head is not the obstacle people expect.
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