Unicorn Theatre, Medieval Abbey Buildings, Checker Walk/Thames Street, Abingdon, OXON, OX14 3HZ Email us if you want travel information. Please be aware that The Unicorn Theatre is part of Abingdon Abbey Buildings - a scheduled ancient monument. There are lots of steps and awkward changes of level throughout the building. Wheelchair access if only possible for some of the events in the building. Please email us for more information. We will always do our very best to overcome access problems. There is no parking for audience members next to the theatre in Checker Walk. There are several car parks a short walk away in Abbey Close, Stert Street and across the river.