I have just found the following on the National Portrait Gallery site :
C.E. Clifford 1849-1886, artists' colourman 1849-1876, photographic materials manufacturer 1857-1865, picture restorer from 1877; C.E. Clifford & Co from 1887, printsellers; C.E. Clifford & Co Ltd from 1912, fine art publishers, printsellers, framemakers, picture restorers. At 30 Piccadilly, London WC 1848-1887, 12 Piccadilly 1888-1891, 200 Piccadilly 1892-1894, 21 Haymarket 1895-1911, 12 Bury St, St James's from 1912, subsequently moving elsewhere
I don't know where "elswhere" can be! I'm beginning to think he might have sold the company to someone else as I sure my grandfather didn't take it over - and his estate was used to provide for his dead son's wife and seven children.......