Slight update on this, I've found a Wheel refurb shop who are willing and do wheel welds.
Place is called Spit and Polish, in Tonbridge, Kent.
obviously they offer no guarantee for the work as you could leave their shop and hit a pothole at 50mph right afterwards, but the work is £69.
and yes he also said, bin the run flats. in his words... "Run flats + BMW =Disaster" "depends how much money you want to chuck down the drain"
hope this is helpful info.
Alloy wheels and tyre discussion