Tax exemption and black'n'white plates are now on rolling 40 year qualification*, MOT isn't (apart from in Eire, I believe). Pre 1960 is the cut-off for MOT exemption, but I think I'd still want an annual safety inspection conducted by an impartial third party motor mechanic anyway if I had a pre '60 classic.
*see pages 10 & 11 on the link below.
https://www.gov.uk/government/upload...ber-plates.pdf