Hi Tasmin,

I am also directly descended from Lucas and Tryphena Birch via Samuel Birch (Lord Mayor of London), Samuel Birch (egyptologist) and Walter de Gray Birch/Maria Carolina de Albuquerque.
The shopfront is no longer at the V & A Museum - it is now stored at the Battersby Power Station and is not on display.
An etching is available if you source Birch and Birch confectionary shop, 16 Cornhill Rd, London.