Members of The Inklings group, Tolkien and Lewis would regularly meet with other academics at the Grade II listed, external venue, which was previously owned by St John’s College.
Work that EIT wants permission for includes repairing and restoring existing windows and cleaning original stonework to prevent it from deteriorating.
“EIT is committed to carrying out sensitive repairs that allows the heritage values of these important Oxford buildings to be celebrated, and once again reopened for residents, tourists and the wider community to enjoy,” it said in a document filed with Oxford City Council.
The authority is expected to decide if it will grant the application for listed building consent over coming weeks.