Introduced in 1956, it replaced the highly successful Austin A30. The name reflected the larger and more powerful 34 hp (25 kW) A-Series inline-four engine, enabling a slightly higher top speed and better acceleration.

The A35 is very similar in appearance to the A30, except for a larger rear window aperture and a painted front grille, with chrome horse-shoe surround, instead of the chrome grille on the A30. Both have 13 in (330 mm) wheels. The semaphore turn-signal indicators were replaced with modern front- and rear-mounted flashing lights. A slightly easier to operate remote-control gear-change was provided. Much of the improved performance is a result of different gearbox ratios. The A30 has the first three ratios close together then a big gap to top (fourth gear). The A35's ratios are better spaced and give a higher speed in third gear.