Plaque

Wikipedia and others describe the building as previously a 17th century chapel, which it clearly isn't.  This 1863 map shows the streets not yet developed and no building on the site at all. The Lancaster Road Congregational Chapel (careful - there's one in Preston) was built in 1865–6 by James Rankin of St. Marylebone. We take that to be the architect but we cannot identify him. Oddly this 1877 map shows the area built up, with terraced housing on this site, but the map looks more indicative than detailed. The 1893 map shows the 'chapel'.

By the early 1900s the chapel was deconsecrated and used by Gems Studio which was set up in 1885 by Julius Gems. The firm had previously been based at 94 East Street (now Chiltern Street) and initially made bamboo & willow furniture and window blinds. It moved quickly into dressmakers forms, mannequin and dummies with an impressive client list (royals and museums). 1898 to at least the 1930s the firm was known as Gems and Grabham. In the 1940s Gems (Wax Models) Ltd provided wax figures to Madam Tussaud's after WW2 fire damage, and worked with the sculptor Allen Jones on his notorious pieces: Hatstand, Table and Chair (1970). 

In 1969, Island Records acquired the building, constructed inside it 2 recording studios and thus established Island Studios together with new offices for Island Records. In 1982 Jill Sinclair and her husband bought the building and established Sarm West Studios. Here Band Aid recorded 'Do They Know it's Christmas?' in 1984.

In 2013 the studios closed and the building was converted into nine luxury flats.

Sources: Wikipedia - Basing Street Studios, Wikipedia - Sarm Studios, My London, CCA Galleries International, Furniture History Society, Adam Yamey, British History Online, Jean Rowe's PhD Thesis: Sculpting Beauty: A Cultural Analysis of Mannequin Design and Fashionable Feminine Silhouettes.