I feel a little ashamed of myself because I actually missed this completely. But a new little tea room appeared at the bottom of Fore St. (where it turns in to New Bridge St.) opening last year. It has a distinct vintage theme, and is bookable for private parties too.
The Hidden Treasure Tearoom looks like a fabulous addition to the amazing selection of places to go in that part of Exeter, and I can’t wait to visit it. In the meantime I am just going to have to satisfy myself with pictures from Matt Austin and their website http://www.hiddentreasure.biz/
Follow them on Twitter https://twitter.com/HTtearoom