I am fully prepared to get flamed here by everyone...but I think some of your criteria conflicts (i.e fuel efficiency, but then you'd like an SUV thing). Stylish? That's often objective.
But with all of that in mind, here goes -
If you're buying a £20k car, you might find a lot of diesel SUVs will come up. My advice is that unless you're regularly doing 30+ miles a day with some of those miles on fast A roads/motorways? Don't do it.
DPF (diesel particulate filter) issues are just not worth it. Short journeys will clog the filter. You're then in the unenviable position of having to spend hundreds having it sorted. Land Rover Discovery Sports are available for your budget, but with the 2.0 diesel, and the problems that throws up, forget it.
Would you consider a hybrid? I think the Toyota C-HR is a hell of a car for the money - reliable, relatively frugal, planet friendly, stylish, and four seats/luggage.
It's a jacked up SUV thing as well if that's important.
The Sportage, Qashqai, Karoq, T-Roc, or whatever other bizarre nams are out there...I don't know. You're going to get a lot of used diesel examples for that money, and do we really need another 1.6 diesel car on the roads especially if it's doing short journeys in urban areas? (apologies if you then come back and say you're rural and towing a horse)