After training as a zoologist at Oxford from 1931-1934 he began a research career at the Strangeways Research Laboratory at Cambridge. Here Abercrombie studied cell population growth and behavior. He notably discovered that animal cells moving through tissue culture will halt when they come into contact with another cell of the same type, with the important exception of cancers cells. This discovery led to new interest and research into the dynamics and growth of cancer cells.
Abercrombie worked in the anatomy and zoology departments at University College London from 1947 to 1970 and then acted as the director of the Strangeways Laboratory from 1970 until his death. Abercrombie is also known for editing the and co-founding the Penguin New Biology textbook.