EON productions, who are the producers of the official James Bond film series are notoriously protective of their property and rarely give permission for clips to be used in other studio's movies for fear of the clips being misused or lampooned. In this case Dame Helen Mirren and director Roger Michell personally asked the Bond producers Barbara Broccoli and Michael Wilson for permission to use the Scene from Dr No (1962) and promised the scene would be used in context and not adulterated in any way. A small fee was paid (which was donated to charity) and Broccoli and Wilson were allowed to view the finished film with the promise of that if they didn't like how the scene was used then it would be removed before release. Fortunately they had no complaints.
Ken Adam, the famous art and production designer, contacted the National Gallery in in London after the theft (in 1961) of Goya's Potrait of the Duke of Wellington (The Duke) to obtain a slide of the picture. This was so he could paint a copy before filming commenced on Dr. No (1962) in the scenes where Bond spots the missing painting, the in-joke being that Doctor No stole it. The actual painting was not recovered until 1965, the subject of The Duke movie (2021). A similar idea of a missing painting in a James Bond film is Modigilianis "Woman with a fan" in Skyfall (2012) and reappears briefly in Madeleine's room in Blofeld's hideaway in Spectre (2015), a painting stolen in 2010. Likewise with Picasso's "Le pigeon aux petits pois" seen in Bond's room at Blofeld's hideaway in Spectre (2015). Both these actual painting were stolen with 3 others from the Museum of Modern Art in Paris on 20 May 2010.
While the film evinces the feeling that mere weeks or months passed between the theft and the return of the painting, it was in fact 4 years between the events. Furthermore Kempton didn't walk into the gallery to return it but rather returned it via a left luggage office and turned himself in a short time later.
The film uses some authentic TV footage from the era regarding news reporting of the theft (ironically some of it from the BBC archives). It also uses some colour footage taken from Pathe newsreels to depict London in the early 1960s.
Jim Broadbent was Roger Michell's only choice for the role of Kempton. Michell said he would walk away from the film unless Broadbent agreed to play the role.