In 1938, the War Office had issued a requirement for a new, better armoured cruiser tank to replace the Cruiser IV. Nuffield's A16 design was found to be too expensive and in 1939 a cheaper A13 Mk III was adopted. London, Midland and Scottish Railway Company (LMSR) designed the hull, Nuffield - the turret and Henry Meadows - the engine. On April 17, before even a single prototype was produced, first 100 vehicles were ordered from the LMSR and soon additional orders followed, with English Electric and Leyland Motors joining the production effort, a total of 1,771 Covenanters were produced. Nuffield was also approached, but preferred to design its own offspring of the A13 line, which became the Cruiser Mk.VI Crusader.

In an attempt to keep the vehicle as low as possible, a low profile horizontally opposed engine was used. However, that left no room for radiators in the engine compartment. As a result, the radiators were moved to the front of the vehicle. The unusual arrangement, combined with rushed design process, resulted in serious problems with engine cooling. These problems meant that the Covenanter could not be employed in the North African Campaign. Instead, Crusader and American tanks were sent to Africa, while all 1,700 Covenanters produced remained in the British Isles.

By late 1943 the Covenanter was considered too weakly armed and armoured to deal with new German tanks. It was decided that neither problem could be addressed without significant changes in the design, so the tank was declared obsolete and all vehicles except the bridgelayer variant were scrapped.

Except for a few vehicles, Covenanters were never deployed outside of the British Isles. The British 1st Armoured Division was equipped initially with them, but when it was sent to Egypt, the tanks were transferred to the 9th Armoured Division. Eventually a handful of vehicles were sent to the desert for service trials. It is not clear if these tanks were ever used in combat. Covenanters were also issued to some Polish units formed in the UK; they were replaced before these units were sent to the frontline. The only Covenanter known to have been lost to enemy action was destroyed by a German air raid on May 31, 1942 in Canterbury.

A few bridgelayers were used by the Australian forces in the Pacific Campaign.