The TR7, launched in 1974 and characterised by its wedge shape and by a swage line sweeping down from the rear wing to just behind the front wheel, was commonly advertised as 'the shape of things to come'. The design was by Harris Mann who also designed the wedge-shaped Princess.

Power is provided by a 1,998 cc eight-valve four-cylinder engine that shares the same basic design as the Triumph Dolomite 1850 engine, albeit increased to 2 litres and fitted with larger carburettors, mounted in-line at the front of the car. Power is 105 bhp (78 kW) at 5,500 rpm, maximum torque is 119 lb ft (161 Nm) at 3,500 rpm. Drive is to the rear wheels via a four-speed gearbox initially, with an optional five-speed manual gearbox and a three-speed automatic available from 1976.

Various British Leyland vehicles were driven by the lead characters in the British television series The New Avengers, produced between 1976 and 1977. Amongst them was a yellow TR7 hardtop driven by the character Purdey. The car was immortalised as a children's Dinky Toy and Revell construction kit.

Quality problems tended to undermine the car's image in the marketplace. This was primarily the result of the poisonous relations between management and workforce and frequent strikes at the Speke factory near Liverpool. Quality improved when production was moved to the Canley plant in Coventry, and later Solihull. However it was too late to save the car's reputation. In its Frankfurt Motor Show preview edition of September 1977, the German magazine Auto, Motor und Sport reported that the engine of a TR7 press car had given up the ghost and "started to boil" while undergoing a maximum speed measurement over a 4 km (2.5 miles) stretch of track as part of a road test. At the time of the report the cause of the problem was still unknown; British Leyland technicians had already been investigating the car, without comment, for nineteen days. Yet another potentially great car let down by the incompetence of British Leyland.

The demise of the TR7 in 1981 (and the Dolomite a year earlier) marked the end of the lineage of sporting Triumph cars,