Vehicles generally become eligible for MOT exemption from the date they become 40 years old, but they must not be substantially altered based on Department for Transport Guidance that can be found here: www.gov.uk/government/publications/historic-classi...a

Where a major component such as the engine or body shell has been replaced because it was more suitable than repair but the car is pretty much standard then this is acceptable. Also allowed are "in-period" modifications which were popular when the car was new. You also have to declare your car MOT exempt and commit by declaration to maintaining it in a roadworthy and safe condition.