The Minor was officially replaced on the Cowley production lines by the Morris Marina (ADO28), which was developed primarily as a response to Ford's top-selling (and in many respects, conservatively engineered) Cortina.
The spiritual successor to the Morris Minor was arguably the ADO16 Austin/Morris 1100 range, which had been launched in 1962 and aimed at the same small family-car market (and actually replaced the Minor in some export markets such as Australia and New Zealand).