Richard Billington & Sons are listed in the Holden directories between 1805 and 1811 - it is likely that they were sucessors to Smith & Billington. 

The duration of the business is uncertain.

It is probable that the principle partner was a 'Richard Billington (1750-1805) who was registered as an Earthenware Manufacturer. In his probate he left just less than £3,500 which was a large amount in 1805. His estate left equal portions to his wife and 4 sons John, Richard, James and William.' (Source: Nigel Billington - 3rd great grandson of Richard Billington).