Nos. 35-38 Aldersgate Street, built by Inigo Jones. From British History Online: “formerly the London residence of the Tuftons, Earls of Thanet. From them it passed into the family of that clever and dangerous political intriguer, Anthony Ashley Cooper, Earl of Shaftesbury." Later it became a tavern, then a lying-in hospital, then a dispensary. There are lots of pictures of it on the web, many at Collage, including a lovely 1879 photograph. By 1810 a lot of the ground floor was already taken up with shop windows.
Building From 1644 To 1882
Thanet House / Shaftesbury House
Incorporated by royal charter in 1854, possibly on 7th April. Still operating in 1928.