I think Limehouse may not be historically accurate in the birthplace strand.
At British History Online, there's an article titled “Limehouse; The hamlet of Limehouse made a parish”
https://www.british-history.ac.uk/london-environs/vol3/pp236-241
“In the year 1730 an act of parliament was passed, by which the hamlet of Limehouse, and part of the hamlet of Ratclisse, both appendages to Stepney, were made a distinct parish, now known by the name of St. Anne Limehouse, or St. Anne Middlesex; bounded by Mile-end Old-town and Poplar (both hamlets to Stepney), and the part of Ratclisse which remains attached to that parish. The boundary in Ratclisse extends along" the Butcher-row and Whitehorse-street. The division of Ratclisse which is annexed to the new parish has no farther connexion with it than relates to the payment of church rates and dues; it is still assessed separately to the other rates, and chooses its own officers.”
"Limehouse" existed in etymology much earlier. But as a town or parish, it didn't administratively exist as early as the origin of the name:—
"The name relates to the local lime kilns or, more precisely, lime oasts, by the river and operated by the large potteries[3] that served shipping in the London Docks. The name is from Old English līm-āst "lime-oast", and appears in a 1335 record. The name is found used in 1417: "Inquisicio capta sup' litus Thomisie apud Lymhosteys pro morte Thome Frank." — https://en.wikipedia.org/wiki/Limehouse#Etymology
