This is one of three churches in Cambridge designed by Ambrose Poynter. After the unusual basilical design of Christchurch (built 1837-9), Poynter returned to a more familiar pattern at St Paul, which was built in 1841. Here (as at St Andrew the Great, built the year after) he took his inspiration from an East Anglian vernacular, and produced a west tower with diagonal buttresses fronting a long aisled nave.
Unlike St Andrew, St Paul is an austere building. In this it contrasts dramatically with the great Catholic church of Our Lady and the English Martyrs, which was built fifty years later and sits looking massive and ornate a little way up the road. At St Paul, Poynter built in the dark red brick he used at Christchurch. Here, it is used in combination with dressings of pale limestone - a combination that accentuates the harsh lines of the tower and buttresses. The RCHM comments of the interior that 'severe economy is evident in the design'. I'm not able to comment on that (unsurprisingly, St Paul is locked without a keyholder listed) but I certainly think that the same is true of the exterior.
Despite that, St Paul has a certain charm. Accretions of vestries, parish rooms and so on have muddled the body of the church and it is difficult to make out Poynter's strong form. The tower, though, is rather fun: the diagonal buttresses rise in five stages to four little crenellated parapets, like miniature versions of those at the top of St Mary the Great or Haslingfield. The windows in the aisles and clerestory are very similar to his work at Christchurch, being deep set and square headed. He abandoned this style when he worked on St Andrew the Great (preferring a more conventional Perpendicular head) but I quite like it; it's not perfect, by any means, but here (more than at either of his other Cambridge churches) we can see Poynter groping towards a fusion of the East Anglian Perpendicular he evidently revered with the great industrial architecture for which his age is justly celebrated. Incidentally, for more on the remarkable Poynter family, you could go and have a look at the entry for Newton.
St Paul is kept locked without a keyholder.