The final outcome:
VW UK agreed to pay the entire cost of rectification at my chosen body shop, as they were of the opinion that the dealer had taken far too long to resolve what was, in their opinion a straightforward issue. They have also offered some goodwill, and will be discussing the case with the dealer concerned, as this has not been a model example of problem solving.
Later the same day, the dealer group's divisional manager phoned me, as I had complained to the group CEO the previous day, and listened to the tale. (I had still by this stage had no confirmation that the dealer was going to do what they said, and pay up). He asked me to have my chosen body shop send him the invoice direct & it would be paid, and apologised for the whole affair. Thanks to the CEO's interest in customer service, it took him less than 24 hours to fix this. He replied to my initial communication within 5 minutes, and promised to have someone contact me to resolve it the next day. All credit to him, he did exactly that.
So, hats off to Mr Daksh Gupta, CEO of the Marshall Motor Group, for being accessible to his customers, and his no-nonsense problem solving. In one day, he did what his dealer couldn't manage in 2 months.