Ok, looked at the work of Carlo Cafferini and Andreas Gursky you linked to, and did a bit of googling. Gurksy's work is mainly done with large format Linhof cameras, so whatever lens choice you go with, it's not going to look the same with an ASP-C format sensor that has no access to movements--at least not with a single shot. And Cafferini may be using something similar, although in his case, I'm more tempted to say he's either pano stitching with a normal or tele lens, or doing perspective correction digitally.
Whether you want a zoom or a prime lens kind of depends on how you plan to use it, and the individual lenses you're considering. Zoom lenses vary their focal length (like your 18-55), while prime lenses have a fixed focal length. They tend to be simpler, mechanically, and often sport wider max. apertures. But whether one is the right fit for you or not does depend on how/what you plan to shoot, working distance limitations, and your budget. In your case, I don't think there's a hard and fast type (zoom or prime) that's better for what you want to do.
Frankly, I'm not sure a lens is necessarily what you need to be looking at here, as much as post production technique, possibly involving perspective manipulation, lens correction, and panorama stitching. The complete lack of distortion is kind of the clue to me that something's been monkeyed with digitally in post, because most lenses with that wide an angle of view don't much tend to look that geometrically perfect or neutral. Panoramas do.
OTOH, you may also be able to do something similar with a tilt-shift lens (the mainstay of architectural photography), but a £200 budget won't get you one of those--they're £1000-£2000 lenses--you might be able to rent one, but they're also not the easiest lenses to master.
You might also try an ultrawide lens, and then correct for lens distortion and perspective in post, but a single shot is unlikely to get you super-high resolution, particularly after you're stretching pixels around in post, so a panorama with a longer lens may be another choice.
Sorry I can't be more decisive on this. I have no idea of what the actual technique and gear is being used. I've just stitched a ton of panoramas and I know that look vs. an ultrawide, and to me the abstract images you linked to look more like perspective-corrected shots.
A number of Cafferini's street shots, though, "feel" to me like 35mm-equivalency type shots, so one possible lens to look at that might actually fall within your budget is the EF-S 24mm f/2.8 STM. But I could be horribly wrong.