There are, I believe, two possibilities for the 'B' mark. It may be a quality indicator, usually 'A1' being the most heavily plated, followed by 'A', 'B' etc. This form of indicator is quite meaningless as it was self controlled and with no official rating, thus one firm's 'B' may well be superior to another firm's 'A1'. The other possibility is that the 'B' is a date code. Some firms, most notably Elkingtons, Mappin & Webb, Walker & Hall, Martin, Hall & Co., and Barnards, used date letters or numbers to identify the year of production.
Below is an example of a Barnard's maker's mark. In this case the '1' is year indicator. You will note that they also used the cross within a shield to identify themselves as a London manufacturer.

Trev.