Purdy,
Not sure what you're wanting to hear, I've explained the situation, you already knew the situation, it appears you went in with your eyes open.
I believe for all intense & purposes it is illegal for you to drive the buggy on the road as the V5C does not reflect what the vehicle is.
Let me ask you a question. Somebody offers you a Ford Focus, they then tell you that they bought 2 Foci the first was a 1.3L the other a 2.0L Supercharged dogs bollocks which was accident damaged. They then took all the parts off the 2.0 & put them on the 1.3 including the reg & vin plates. They are then selling the 1.3 as the 2.0, would you buy this & run round in it, if the answer is no, then surely the answer to your Blitz issue is no.
I'm not sure you grasped the insurance bit though, you may insure it as a Blitz but in the event of an accident, they may use the fact that it's still registered as a Mini not to pay out, there is possibly more of a risk if you actually get hit rather than doing the hitting.
I would hazard a guess you could probably run around as it is for many many years without being bothered by anyone, but as stated before there will always be that risk
Just remember these are just my views, because of that it doesn't make them right, you have to do what you feel is right.
You may get more 'robust' answers from other members, don't take it too personal if you do.
Alan...