Not got BS7671:2001 to hand, but know BS7671:2008 stipulates a minimum of 16A supply, it is not retrospective, so if has been 6A for over 10 years there is nothing to say they must upgrade, and BS7671:2008 is not law anyway, although it can be used in a court of law.
I know my caravan has a 10 and 6 amp MCB fitted, so in theory van trip should go first.
As to an "ordinary person" accessing a locked distribution unit there are clearly issues, even as a "competent person" or "skilled person" there would still be issues accessing a distribution unit. But main point is a consumer unit is a type tested distribution unit designed so an "ordinary person" can reset MCB's or RCBO's or swap cartridge fuses, unless it has the BS number and I don't of hand know what that number is, to leave it unlocked could get the site owner in trouble from HSE, and typically a 16A fuse costs around £2 to £3 so it is not unreasonable to charge for the replacement.
If not a cartridge fuse but rewire-able, then the person changing the fuse must be trained, i.e. it may not be the site owner, he may be forced by HSE rules to call out an electrician.
Remember it is not his home, he has to satisfy HSE inspectors and insurers, and he does not really have a clue as to who is using his site, for all he knows you may be a HSE inspector, so he has to keep to the rules.
Clearly if the fuse/MCB/RCBO is less than 16A he is up the creak as far as charging goes, unless he explains as you book in there is less than 16A, also all his adverts for the site would need to say what the power is, if not 16A, however if I was told sorry either no electric or 5A only then I would still stop on site with 5A only in the summer.
I think I have stopped on sites with locked reset box, and I have tripped it, however there was more than one socket on box so simply swapped plug to one which had not tripped.
I have never been charged for a blown fuse, I think if I was then I would simply not return to that site, back in the late 90's I did stop on a site with a 100 amp split phase supply to site, if everyone is using an average of 10A that is only 20 vans, he had more like 100 vans so limited the supply to 5A, people did all sorts to get more, fit a 15A MCB live working and scrape off the 1 so it looked like a 5A, turn the screws in the 5A so it would give more, hard wire across the MCB, I really could not believe what people would do, risking their life in the process.
Then the main incoming fuse would blow, that needed a visit from the DNO to replace it, so everyone lost power over night because of the greedy few, I helped the site owner fitting two 80A MCB's so they went before the main fuse, then it was a case of finding the fiddled outlets, we used a 2 kW fan heater, if the MCB did not trip it was changed, end of the day he had a box full of MCB's around 30 had been one way or another fiddled to get more power.
The electric was not the only problem, some one had found a device to kid the telephone into thinking it was a 999 call, he was selling these devices at work, but the Post Office realised what was going on, and were modifying public phone boxes so they would not work any more, however the site phone was owned by the site owner, the 99 fiddle made the phone work without money, but did not con the exchange, so the owner had a huge bill, with very little money in the phone box.
I am sure all in all he made a lot of money off the contractors using the site for 4 years while the power station was built, however he also had a hard life with all the tricks being played on him between one thing and another, and he likely also lost a lot of return custom for years latter once back to a holiday only site.
The site is still going today, but I bet if there was every another power station built he would think twice before letting contractors in.