Maurice Cockrill studied at Wrexham School of Art and the University of Reading between 1960 and 1964. He lectured full time in the Faculty of Art at Liverpool Polytechnic from 1967 to 1980 and was a visiting tutor at Schools of Art in Manchester, Portsmouth, Farnham, Winchester and Nottingham between 1982 and 1985.
He went on to become a Visiting Tutor at the Royal College of Art and Central School of Art from 1985 to 1988. He was Visiting Tutor at Saint Martins School of Art from 1984 to 1994. In 1995 he was Artist in Residence at GOFA University of NSW, Australia, and was Visiting Tutor at the Royal Academy Schools from 1994 until 1998.