Mdthbs

The expression “shotgun wedding/marriage”, as described in the following link, is an AmE 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 first appeared 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 England?

knobstick wedding Wikipedia

A knobstick wedding is the forced marriage of a pregnant single woman
with the man known or believed to be the father. It
derives its name from the staves of office carried by the church
wardens whose presence was intended to ensure that the ceremony took
place. The practice and the term were most prevalent in the
United Kingdom in the 18th century.

Here one could experience the blows of the knobstick is this forced nuptial covenant was ignored.

From the OED: now obselete, but was used before shotgun wedding.

knobstick wedding n. now historical a wedding forced on a
couple by parish officials when the woman is pregnant (typically to
limit the number of claims on the poor rate for children born out of
wedlock);

Nowadays, British English speakers may also use "shotgun wedding."

The British National Corpus has a large number of samples of British English through the mid-1990s. Here are the three results that come up for shotgun wedding.

. Of course somebody, Who Shall Be Nameless, would bring up the subject of Burns-And-You-Know-What, and how many of his children were born on The Wrong Side Of The Blanket, What Right Had We to look down on Brown Owl for her shotgun wedding when we were all supposed to look up to Rabbie Burns as Our Big Hero? (True Confessions and New Cliches. Lochhead, Liz. Edinburgh, Polygon Books, 1985.)

There was some speculation about alternatives, with some canvassing the claims of Derby and Salisbury and others imploring Lloyd George to take over the leadership and unite the parties in a shotgun wedding, but Austen's claims were undeniable. (John Ramsden, The Age of Balfour and Baldwin 1902-1940. Longman Group UK, 1978.)

In this sense May 1968 was the price de Gaulle paid for his attempt at a shotgun wedding between French industry and the twentieth century. (John Harrison, Andrew Glyn, and Philip Armstrong. Capitalism Since 1945. Oxford: Blackwell, 1991.)

Notably, the latter two examples use shotgun wedding figuratively in political contexts to describe forcing together two disparate groups for the sake of appearance or political exigence. The fact that they're used, in a way that presumes familiarity by the audience, suggests the phrase is known and used among British English speakers. The Hansard Corpus, a corpus of British parliamentary records from 1803 to 2005, features the usage several times starting in the 1950s:

We have to suffer or enjoy sharing the service with Northern Ireland; it is a marriage of convenience, or perhaps a shotgun wedding, but we should like a divorce from Northern Ireland as quickly as possible (23 May 1957, House of Commons, Mr. George Chetwynd)

The corpus has 29 results total, and the usage seems about equally common from the 1960s onward.