From Longman Dictionary of Contemporary Englishshut something in the door/drawer etcshut something in the door/drawer etcBritish English, shut the door/drawer etc on something American EnglishSHUT/CLOSE to shut a door etc against something so that it gets trapped there I shut my finger in the back door yesterday and it still hurts. → shut
Examples from the Corpus
shut the door/drawer etc on something• Madeleine grimaced after she'd shut the door on him.• It watched her, unwinking, until she reached the room behind the shop and shut the door on its crimson gaze.• Come in, lads, come in and shut the door on the fog.• Even so, Wickham was not ready to shut the door on the possibility.• Everyone has been going for national contracts and that has shut the door on the small company. 