There are several methods.
1. Saturate the bolts with a good penetrating oil, tap the bolt several times to shock the threads / assist with oil penetration. Leave for a while then try using a good set of mole grips or your extraction tool again.
2. Apply heat to the base of the bolt using a flame , I use Oxy acetylene but you may be able to do it with a butane torch? I usually get the bolt cherry red before applying grips again.
3. I have also managed to remove a broken stud by mig welding an oversized nut to the broken bolt. This has a dual purpose of transferring heat into the bolt / housing and also allowing a socket to be used for removal.
4. If all else fails, as a last result you can drill down through the centre of the bolt and re- tap a new thread.
If you were closer, I’d offer to help but did it to Worcestershire area is a bit far.