Very sorry to hear of your problems with the Mini.
But don't lose heart. There is a lot of help and encouragement on here.
I am not a lawyer, but I've been around business and the law for many years and my take is as follows:
You bought the car in good faith from a dealer and you are not a qualified person in terms of assessing the condition prior to purchase. The dealer has, by selling the car to you, made certain claims as to its mechanical condition even though he may or may not have put this in writing. He is deemed to be an expert.
You are fully entitled to expect the car you bought to perform well and to be safe and reliable for a reasonable time. For an older classic car it might be expected that some minor mechanical issues might crop up, but what you have (from what you have said) is a level of structural corrosion which could not have arisen during your time of ownership. A 12 month period might well be felt reasonable for corrosion issues.
It would be advisable to return to the vendor with the car and, most importantly, with someone who really knows their way around the Mini range and the problems with corrosion. You need someone on your side to help point out the issues and to discuss how they would have existed at the time of purchase.
Then see what the vendor offers. He may offer to do the work at no cost to you, or he may politely (or not) tell you to 'go away'. Either way you can then decide on your next step.
If the vendor offers to do the work have your independent expert discuss the full schedule of work needed, which you will need anyway whatever happens.
Should there be no offer of recompense my advice would be to find a solicitor specialising in consumer law. I've never found the CAB to be much use as they are not legal professionals and will not have the experience to be of any real help.
In the worst case you can issue County Court proceedings asking for a full refund. With a full independent report, supported by photographs, you will have a good case.
Be very professional with this and go one step at a time. Record everything and have full details of everything you do and all defects you and your expert finds. It may be that there are bits of corrosion you have not yet identified. From my own experience with a 1997 MPI which had 8 months MoT the rust can be very deep rooted.
If I lived nearer I would be pleased to do the assessment, but I'm sure there is someone on here much nearer who could help.
Good luck with this and if we can all help you that will encourage you not to let go of this. You will certainly get at least some of the costs back, or a full refund.