Hutch, it's not really to do with the EU. Any vehicle which is not otherwise exempt must have an MoT; that's always been the law since roadworthiness testing was introduced. The Goods Vehicle (Plating and Testing) Regulations have an exemption for vehicles manufactured before 1 January 1960, used unladen and not drawing a laden trailer. More recently, harmonisation with EU regulations meant that this was extended to all pre-1960 vehicles, not just goods vehicles.
Brooky obviously assumed your Militant was pre-1960 which is why his question - and indeed it may well be, but the licencing authorities often use the date into service (DIS) given by the MoD as the date of manufacture, and in reality the two are not always the same. I'd guess your 1966 date came from MoD disposal documentation, or the previous owner?
You're right that this might now change; further EU harmonisation has resulted in a consultation, which ended last month, about further changes to the law. The option favoured by the Ministry is to change to a rolling 40 year exemption, which would make pre-1976 vehicles exempt as of current date. However there may be some wrinkles to it, as there is some thought of introducing a basic safety test, and scoring vehicles for originality per the procedure for registering heavily modified and kit built vehicles.
The proposed changes are here:
https://www.gov.uk/government/consultations/roadworthiness-testing-for-vehicles-of-historic-interest