A final set of designs produced sometime between 1740 and 1748 shows a new building to the west of Westminster Hall with a uniform frontage to St Margaret's Lane. This building incorporates the Law Courts adjoined to the west side of Westminster Hall (the Court of Commons Pleas of 1740-41 was by Kent or Isaac Ware), and is sometimes parallel to, and sometimes sits at an angle to, the medieval hall. In addition, a more economical Parliament House is shown to the south-east of the site, linked by long corridors to the old and new Courts of Requests and with a wide range of offices along the south side. Nothing came of the final Parliament House scheme, but Kent's designs for a new building to the west of Westminster Hall formed the basis of the Stone Building which was built by John Vardy between 1755 and 1770.

(Salmon, pp. 352-55)