VW Tiguan (2.0 diesel)

VW Tiguan (1.6 petrol - yet to find one suitable within budget)

Not surprised at this myself seeing as the Tiguan has never been available with a 1.6 petrol!. Closest to a 1.6 has been the 1.5TSI which first appeared in 2019 (replacing the excellent 1.4TSI) along with various problems typical to VAG rushing stuff onto the market without developing them properly. So if you could afford one of these (circa £22k+), you'd be better going for a late 1.4TSI.

Seat altea/Altea XL (although I think this is probably bigger than what I need!)

The larger of these, the XL, is only 4cm longer (and slightly narrower) than the 1st and 2nd gen Tiguan, so can't imagine why it would be too big?. But all the ones on Autotrader are diesel, which is not ideal(*). I might be tempted by a well loved 1.9, possibly a 2.0, but I'd give the 1.6 a definite swerve.

Seat ateca (seems beyond budget)

They only came out in 2018. Cheapest on Autotrader is just under £9k, there is one other at £9.5k but the rest are over £10k.

But TBH, I'm not sure I'd be overly keen on most VAG options at your budget, too many iffy engines to sift though.

Kia sportage

You shouldn't have too much trouble finding a decent Sportage at this price. Problem is most are diesel(*) with the rest split between a n/a 1.6 petrol or a n/a 2.0 petrol. The 1.6, while certainly reliable and having a reasonable amount if power on paper, is a bit lacking in torque for a quite heavy car. So if you are a press on type of driver, you will probably find its performance frustratingly flat unless being ragged senseless (in which case the MPG will really suffer). The 2.0 is also reliable, but I doubt the economy would be anything to write home about either.

Suzuki Vitara is also worth considering.

With reasonable miles (up to 80k), there are 7 nationwide on Autotrader, so chances of finding one local are very slim. The SX4 S-Cross is mechanically identical, has a usefully bigger boot and there are more of them within the OP's budget (though still not exactly 10 a penny).

*At the OP's budget, a diesel is going to be getting on but will also most likely have some kind of equipment to reduce emissions (which started to appear around 2007 I believe), most commonly a DPF. These can cause very expensive problems, especially if the car has been used for shorter journeys. Reliability in general can suffer, especially with the aforementioned shorter journeys, but also re servicing with many diesels causing problems unless very specific oil is used. In short, the risk in buying a diesel is quite high, so unless you really want, or feel you really need a diesel, probably best to avoid.