Background sources on the TR2 can be found here and here. They don't give a date when the design and engineering processes for the TR2 began, but it was probably around 1950, two years before the car was revealed at the 1952 Earls Court Motor Show. The TR's market niche was between the MG T series and the Jaguar XK120, a wise decision.
Standard Motor clearly thought a Triumph sports car launch was risky, so body fabrication was made as inexpensive as possible. The result was ugly styling. Even so, the design didn't seem to hurt TR2 sales. The car was peppy and got good reviews, so apparently buyers disregarded the car's looks.