In the late 1970's Martin Lilley decided that a completely new model would allow TVR to broaden its appeal, and ex-Lotus designer Oliver Winterbottom was commissioned to design a new car. This was a major undertaking because up to this point all previous models had evolved from the first production car, the Grantura. The car had an all-new chassis, courtesy of another ex-Lotus designer, giving a longer wheelbase and increased rigidity. Due to the origins of the designers both body shape and chassis bore more than a passing resemblance to the Lotus Elite and Eclat. Pop-up headlamps kept the wedge shape tidy when the lights were not in use. Three models were announced at the same time - a fixed head coupe, a 2+2 coupe and a convertible. A 160bhp Ford Cologne V6 of 2792cc gave good performance and all models had a walnut dashboard as standard for the first time. The convertible's roof had a hard centre panel and a folding rear section, a feature still used by TVR today. Early sales were slower than the outgoing M series, and the Tasmin was more expensive. By 1982 Peter Wheeler had taken over from Martin Lilley, and the cheaper 2.0-litre Tasmin 200 was launched. This was not popular however and it was phased out in 1984. In 1982 a turbocharged version of the Ford V6 was developed, but 1983 saw a development which has been a major factor in TVR's subsequent success.

The 190bhp alloy V8 engine used by Rover was fitted to the Tasmin, producing the 350i. At the same time, the Ford engined cars were renamed 280i. Changes had to be made to the chassis to fit the Rover engine, which also improved handling substantially. Straight away the 350i convertible became the best selling model. In 1984, the 390SE was introduced. This had a 275bhp blueprinted 3905cc V8, and serious performance to match the high price - 30% more than the 350i. A deeper front spoiler and a rear under-body aerofoil were the obvious external changes. In 1985 the series 2 cars appeared. Changes to the bodywork softened the sharp edges of the wedge shape to make the car more attractive, and in 1986 revised rear suspension improved handling.