The expression “shotgun wedding/marriage”, as described in the following link, is an American English one.
Of American-English origin, the phrases shotgun wedding and shotgun marriage denote a wedding into which one or both partners are forced, usually because the woman is pregnant.
Its earliest usage instances appear to date from the second half of the 19th century from American papers such as:
The Cincinnati Enquirer (Cincinnati, Ohio) of Monday 15th April 1872 and
The Telegraph and Messenger (Macon, Georgia) of Tuesday 21st August 1883.
Also its metaphoric usage appears to have been first used in AmE:
Those phrases came to also denote any forced union. The following article from the Editorial Page of the San Francisco Examiner (San Francisco, California) of Friday 1st March 1929 illustrates the transition to this generic sense.
I’d assume that in the 19th century this kind of marriages were celebrated in England too, and if so, what were they called in BrE?