 The church of St Paul 's was the first building , and was begun in July 1631 on the western side of the square . The last house was completed in 1637 . Seventeen of the houses had arcaded portico walks organised in groups of four and six either side of James Street on the north side , and three and four either side of Russell Street . These arcades , rather than the square itself , took the name Piazza ; the group from James Street to Russell Street became known as the " Great Piazza " and that to the south of Russell Street as the " Little Piazza " . None of Inigo Jones 's houses remain , though part of the north group was reconstructed in 1877 – 79 as Bedford Chambers by William Cubitt to a design by Henry Clutton . 
