Since 1937 Babmaes Street has been the name of the street previously called Wells Street and of the yard to which it leads from Jermyn Street, previously called Babmays (corrupted to Babmaes) Mews.

Babmays Mews was laid out on the St. Albans freehold at the same period as St. James's Square, on a plots of ground 200 feet square. From the first it was intended as stable yards for the houses built on the St. Albans freehold and was known as the East Stable Yards. The parts adjacent to the backs of houses in the square were held with those houses, but neither stable yard communicated directly with the square.

The East Stable Yard, unlike the West, was approached by a fairly wide street called Wells Street, linked with Piccadilly by Eagle Street. Wells Street, which was not part of St. Albans's freehold, first appears under that name in the ratebooks in 1671. It was presumably laid out by John, George or Francis Wells, the first a victualler of St. Marylebone and the others perhaps a bricklayer and a carpenter. The yard itself by the time of Rocque's map was called Babmay's Mews, a name clearly deriving from Baptist May. Rocque's and Zachary Chambers's (and earlier) maps show this as an open rectangular yard. Rhodes's map of 1770 shows an isolated block in the centre and by the time of Thomas Chawner's map of 1794 the open space had been reduced approximately to its present form.

Until recently Babmaes Street was used in part for the modern equivalent of their original purpose. Babmaes Street had been almost wholly transformed in appearance, and the centre of the former Babmays Mews is now being rebuilt as offices with a garage in the basement.