This car, in only its second event, gave Paddy Hopkirk and Henry Liddon outright victory in the 1964 Monte Carlo rally, beating Ljungfeldt's Ford Falcon into second place and Eric Carlsson's Saab 96 into third.

Cooper driving team-mates Timo Makinen and Rauno Aaltonen finished fourth and seventh respectively, and the BMC team gained the manufacturer's prize. No fewer than 38 of the 342 entries in the Rally were Mini Coopers.

33 EJB was one of the first 1071cc Cooper S models and was prepared to FIA Group 2 specification for the Monte Carlo rally meaning the bodywork remained standard but some engine tuning was allowed.