Barclay graduated with a Bachelor of Arts (BA) degree in Natural Sciences from the University of Cambridge. For a postgraduate study, she conducted medical research at the Common Cold Unit in Salisbury, supervised by David Tyrrell and Fred Brown, for which she was awarded a Doctor of Philosophy (PhD) from the University of Reading in 1988: her doctoral thesis was titled "The humoral immune response to rhinovirus infection". At Reading, she was involved in human challenge studies with rhinovirus, to study the virus and its interaction with the human body.
