Do I need planning permission for a garden room in Cambridge?

Often you will not, but Cambridge is one of the places where the exceptions bite hardest. The standard rules allow a garden building without permission provided it is single storey, sits behind the front wall of the house, covers no more than half the land around the original house, and stays within 4m overall for a dual pitched roof, 3m for anything else, or 2.5m if any part comes within 2m of a boundary. Conservation area status, listed buildings, flats and Article 4 directions all change that answer, and Cambridge has more of all four than most cities.