"as I stepped quickly along towards Headingley"
Madingley Hall in Madingley, Cambridgeshire
Public DomainMadingley Hall in Madingley, Cambridgeshire - Credit: Ben Mills, Wikimedia Commons

Headingley is the fictional version of Madingleya village situated on the outskirts of Cambridge. The road named Madingley Road heads out of Cambridge in the direction of Girton College, the all-female college (at least, when A Room of one's own was written) on which the fictional Fernham is partially based. Girton is situated about 2.5. miles northwest of Cambridge city centre.

The name Headingley does exist as the name of one of the inner suburbs of Leeds.