Using a MX5 rear end on a registered kit, IVA ?

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I'd start with the thought that no one is ever going to pull you over to check whether you have a live axle or IRS and no MOT tester will be interested. Though a V5 will show engine size and if it has auto transmission there is no entry for axle type

So long as you haven't changed chassis number there is nothing to worry about. Lots of people upgrade rear axles on classic cars to improve ride and handling. So long as the work is done well, the welding is sound and the brakes work it will be fine.

Its really only if you are changing chassis or very substantially altering an existing chassis that one needs to consider another IVA.