Came here to ask the same question. It certainly looks very similar, and I think Marina's car is definitely also a cut-down mini; but I don't think it's the self-same car. It would be nice to know where the actual one is.
First and foremost, it's a different reg; Marina is driving SHD562X (1981 reg letter); I can't read the full flickr reg, but it starts D319... (1986 reg letter). Second, if you look closely, there are minor differences. The flickr one has the winged mini badge, whereas Marina's badge looks more like a shield; the flickr one has a tonneau cover behind the seat, wheras Marina's doesn't. The seatbelt attachments are different. And the chrome around the rear light cluster (and possibly the rear lights themselves) look like they may be slightly different as well. Obviously none of that is definitive - the registration could have been changed, and anyone who owns a car like that is likely to lovingly maintain it and possibly tinker with its details - but they certainly suggest two different vehicles.