I think the dimensions on this site are excluding mirrors (rather than with them folded) and with them extended. However in the OP's case that will make no difference (unless planning to push the car into the space!) as the car will (presumably) be reversed in using the mirrors to get as close to the wall on the passenger side as possible, then opening the drivers door to get out.

Narrowest "conventional" car I can think of is the Kia Picanto at 1595mm (the Picanto's sister car, the Hyundai i10 is 65mm wider).

If that is just too small, then the Honda Jazz would be an obvious choice at 1695mm while also being extremely spacious (and flexible) and extremely reliable.

Same width as the Jazz but with slightly less interior space is the previous shape Toyota Yaris (current shape is 50mm wider). Same width but slightly less interior space again would be the Mazda 2 (not the rebadged Yaris). Both of these also extremely reliable.

Other cars in the same class are going to be wider but not by a huge amount. You'd generally be looking at between 1730 and 1770mm.

The Skoda Rapid/Seat Toledo mentioned by Andy are indeed very narrow for their size at 1706mm. They have a particularly spacious rear seat (best for two because of the narrowness of the cabin) due to having such a long wheelbase (distance between the centre of the front an rear wheels) and they also have a huge boot. So if adults are regularly carried in the back and/or a big boot is needed, one of these could well be your best choice.

If you need more than 5 seats, and you can find one (they are like hens teeth!), the car version of the Nissan NV200 van as 5 or 7 seats but is the same 1695mm width as the Jazz. Electric versions of these (eNV200) are also available (and more common) but are listed as being slightly wider at 1735mm (I think the wings are different).

If you are open to the notion of a Japanese import then a whole world of narrow options present themselves, with the Kei car at the bottom. These will be no more than 1480mm wide, no more than 3400mm long and have a 660c engine of no more than 64bhp. So clearly not a car for family holidays or motorway commutes(!), but as a town/city runabout, there can be few narrower cars. Plenty of MPV's of the same with as the Jazz, Toyota Noah/Voxy, Honda Stepwagon and Nissan Serena spring to mind.