Southampton Street, Strand, was so called in compliment to Lady Rachel Russell, daughter of Thomas Wriothesley, Earl of Southampton, and wife of William, Lord Russell, the patriot. Eminent Inhabitants. – Mrs. Oldfield, the actress; Arthur Maynwaring, in his will, (dated 1712), describes her as residing “in New Southampton-street, in the parish of St. Paul’s, Covent Garden.” David Garrick in No. 36, before he removed to the Adelphi; the house has been new-fronted, but remains, I am told, much the same inside as when Garrick left it.
Source: A Handbook for London, Past and Present. Peter Cunningham. Published by John Murray 1849.