An updated version of the Pinin Farina designed Cambridge, originally launched in 1959 as the A55 and now called the A60, was introduced in October 1961. It included a new 1.6-litre version of the B-Series straight-four engine which had first been used in the MGA. Modified styling included side chrome stripes – some models with contrasting colour in fills – and reduced fins on the rear wings. The style continued to be known as "Farina". The chassis was slightly longer in wheelbase and wider in track than the A55. This allowed three people to be accommodated on the rear seat. An estate version called the Countryman, was also released. From 1966 the A60 was offered with many optional extras including a more powerful twin carburettor version to keep up with increasing competition from the Continent and Japan.

The A60 Cambridge sold well, with 276,534 being built before production finally ended in 1969. Its intended successor, the front-wheel-drive Austin 1800 of 1964, did not affect sales, so Cambridge production was continued until 1969 at the Morris plant at Cowley when the Austin Maxi took over production line. The Morris Oxford version continued in production until 1971, when the Morris Marina was launched.