The British consulates in China are not yet individually accessible on this website, but the last menu option on the right leads to an overview of the history of all the consulate buildings in China.
These two sources, especially the first, have been invaluable in piecing together the Beijing entries:
Hoare, James E., Embassies in the East: the story of the British and their Embassies in China, Japan and Korea from 1859 to the present, Richmond: Curzon, 1999.
The Old British Legation at Peking 1860-1959, based on a lecture delivered 20 August 1962, J.L. Cranmer-Byng