Looking further, and without any useful specification on the VW website, I think that I have found why it's not charging at more than 16 A.
The CCS connector on the car has three power pins, N, L1 and L2. L3 is absent.
I think that the car is set for mainland European mains power, where three phase is far more common, but the current rating is less than the 80 A that is common in the UK. It seems that the car can charge at 3.6 kW (16 A) on each of two phases, giving a total of 7.2 kW. I can only provide one phase so it's limited to 3.6 kW
Cars with single-phase 7 kW chargers will only charge at a lower rate where there's a domestic 3-phase supply limited to 25 A or less. Some cars have changed to 3 phase inputs in later model years so that they can be charged at up to 11 kW on a 3 phase 16 A supplies.
Also, I've heard that new build houses in the UK will be getting 3 phase supplies in future, but I don't know the details. The intention is to make EV charging, heat pumps, microgeneration and domestic energy storage easier.