1921–1926 (pp. 58–106),
1926–1930 (pp. 58–102),
1931–1935 (pp. 52–92),
1936–1940 (pp. 31–51),
1941–1945 (pp. 65–90).
Click "Preview an image of the this record" and leaf through the document to the pages indicated above. The documents are not OCR'd or searchable, but easy to use, since the names are organized in the alphabetical order and Shanghai records are always in the final pages. Not all registrants are UK citizens! There are many Russian and European names.
For example, these are the names starting with A and B, registered in the years 1936–1940:
Whose name goes first and why? We see Mr Ibhahim K. Abdom marrying Miss Musienko, Mr Frederik Adams marrying Miss Crosslend, Miss Irene Afichuk marrying Mr Sergeefff, Miss Valentina Alania marrying Mr Rosen, Mr Walter Allan marrying Miss Harmon... Mr Alexander Becker marrying Miss Bredinina... Miss Tamara Bredinina marrying Mr Becker... Aha! Each marriage is recorded twice, by her name and by his name. Duh.
These short records are provided by the National Archives at Kew, but full records are viewable only on commercial genealogy websites.