Hmmm. I thought I had an answer for you, but then I noticed the film was set in Glasgow.

Broccoli has been a commonplace vegetable in Italian cuisine since the 18th century, and was introduced to the United States as early as the 1920s; there's a fairly famous 1928 New Yorker cartoon about a kid rejecting this new fad vegetable. ('I say it's spinach, and I say the hell with it.') George H.W. Bush (b. 1924) complained in 1990 of being forced to eat broccoli as a kid and refusing to do so now that he was president, and a quick glance at the NYPL Menu collection turns up hundreds of examples from the 1930s on.

The UK, however, is a different story. I don't know much about broccoli availability specifically. But wartime food rationing didn't completely end in the UK until 1954, and many vegetables that would now be regarded as commonplace were considered exotic in post-war England. The food writer Elizabeth David had a series of popular cookbooks in the 50s and 60s which helped introduce UK home cooks to Mediterranean-style cooking, but often the dishes she was talking about would have been utter novelties to English and Scottish readers and many of the ingredients would have been difficult or impossible to obtain in a typical supermarket. (You were more likely to find olive oil at a pharmacist's than a grocery store, for example.) Bit of digging shows David's 1954 Italian Food contains a single broccoli recipe, but no clear indication of whether that's a vegetable that'd be easy for her contemporary readership to find.

Happy to be corrected, but my guess would be that broccoli might have still been a bit posh and unusual in Glasgow in the late 70s.