[1][2] The Barrett Room at Addenbrooke's Hospital is named in his honour, as is a Prize for the undergraduate Part II Pathology Tripos at the University of Cambridge.

He won a Raymond Horton-Smith Prize for his MD degree thesis in his later life (submitted in 1960) on estimating the increase in heart weight by quantifying the examination of the arteries.

By use of his “undulation index” Barrett took full account of the degree of post-mortem contraction of arteries, a factor which had vitiated so many previous investigations.

Barrett’s solution of this problem was a notable advance in angiology, and helped in transferring histological observations from the art of opinion and impression into the exact science of quantitative measurement.

[6] He worked in the wards and laboratories of the London Hospital from 1934 to 1938 and was University Demonstrator in Cambridge from 1938 to 1946, the only one in the Department of Pathology during the war years, having a large part of the teaching responsibility.

[8] Later a venue in a private ward at the Addenbrooke's Hospital in Cambridge, used for seminars, training, meeting, consulting and conferences, was named Barrett Room in his honour.