Laws was born in Whitley Bay, Northumberland and educated at Dame Allan's School, Newcastle upon Tyne, and St Catharine's College, Cambridge, where he was an Open Scholar.
He started his career as a zoologist on the Falkland Islands Dependencies Survey in 1947, where he investigated the ecology of elephant seals in the South Orkney Islands and South Georgia. These formed the subject of his 1953 Cambridge PhD. After spending a season as a whaling inspector, he joined the National Institute of Oceanography 1955-1961 where he studies great whales and elephant seals.
Outside Antartica, he was also an expert on large African mammals. In 1960 he was appointed Director of the Nuffield Unit of Tropical Animal Ecology in Uganda. Over the next eight years his research focused on hippopotamus and elephant ecology. He spent a year as Director of the Tsavo Research Project in Kenya 1967-1968.
He returned to Cambridge in 1968 to resume his Antarctic research. In 1969 he became Head of the Life Sciences Division of the British Antarctic Survey. He became Director in 1973, a post he held until retirement in May 1987. He was Secretary of the Zoological Society of London 1984-1988. He was Master of St Edmund's College, Cambridge 1985-1996, and he was a member of the Scientific Committee of the International Whaling Commission.
In 1954 Laws won the Bruce Memorial Prize for his work on the ecology of elephant seals. He was awarded the Polar Medal in 1975. He was elected a Fellow of the Royal Society in 1980, and was appointed Commander of the Order of the British Empire. In 1991 he was awarded an Honorary Doctor of Science degree by the University of Bath.
On his retirement, a fund was established for a prize to be awarded in recognition of the achievements of outstanding young scientists of the British Antarctic Survey. The Laws Prize continues to be awarded annually.