Scam? As far as I know, changing the incoming fuse to 80a is free or a minimal fee like £50, depending on the DNO, but you would not be charged £1300.
We were unlooped and a new cable laid to the property, complete with new 100a fuse holder for free. DNO was SSE.
Phone the DNO and check with them, I’d be very suspicious of any unsolicited e-mail “quote” with incorrect details on it. If it is correct then what are they going to be doing for the £1300?
At £1300 you’d be cheaper ignoring BP & getting a charger fitted at your cost with a built in load limiter so your 60a fuse can remain. It would throttle the charger whenever load on the main is close to 60a. Basically unless you are up at night cooking, cleaning & using electric showers then it would charge in the wee hours without any issue – most after 1am electrical loads on the house are minimal – fridge, odd light etc unless you have Economy 7 heating or have load shifted your washing machine/tumble dryer. The Viridian unit I purchased has this built in, its costing me £500 fully fitted (its not OLEV grant eligible).
In life, it's not who you know that's important, it's how your wife found out.