Neil Jordan originally intended to title the film "The soldier's wife", however he was advised by his friend Stanley Kubrick to change it. Kubrick recommended this change because he believed that films with either religious or military titles usually deterred audiences and were often financial failures (something that Jordan had experienced when his religiously titled movies The Miracle (1991) and We're No Angels (1989) flopped at the box office). Jordan selected the new title title from a 1960s hit British pop song.
Producer Stephen Woolley owned a repertory cinema in London called the "Scala", when there were funding issues with the film Woolley ended up borrowing money from the Scala to keep the production afloat.
The trivia items below may give away important plot points.
A few weeks into filming, Jaye Davidson got ill from flu. A doctor was called to the set to take a look at him. The doctor entered Jaye's tiny trailer, examined him and came out to talk to director Neil Jordan. The doctor asked Neil "Have you considered the possibility that she might be pregnant?". To which Neil and the other crew began to laugh. The doctor looked bemused, and was only let in on the secret a few minutes later. He felt very foolish.
The casting of Dil proved extremely difficult for the filmmakers (Stanley Kubrick had at one point warned Neil Jordan the role was probably uncastable) until the casting director (Susie Figgis) received a tip-off from director Derek Jarman about Jaye Davidson. Davidson was later "discovered" by the film's casting agents at a wrap party for Jarman's film Edward II (1991), and was offered the opportunity to try out for the role of Dil. Davidson was (by his own admission) very drunk and not particularly enthusiastic (he thought it was just a joke at first) but eventually took the role in order to pay for a pair of hand-made leather riding boots he had seen in a copy of Vogue magazine.
Although producer Stephen Woolley was immediately taken with Neil Jordan's script, he met with zero interest in America. The general consensus was that the Jaye Davidson role was uncastable, and the film's mix of sex and terrorism would prove unpalatable with audiences. And that the press would divulge the film's big twist. Eventually Woolley was able to drum up the necessary budget from British, European and Japanese sources, but then had to contend with the financial collapse of his production company, Palace Pictures. When Miramax, who had initially rejected the script, saw the finished product, they immediately made an offer to distribute the film in the USA, with a clause in the contract that they would push the film for Oscar consideration.