Regardless of budget, this is a difficult set of criteria to meet. Much smaller than a Qashqai (itself not that big), tall, fuel efficient and comfortable.

When you say much smaller than a Qashqai, that makes me think smaller than a Fiesta or Polo, i.e the 'city car' class. In which case, the Ignis is the obvious choice. But, isn't easy to make a very small tall car that comfortable due to the physics involved with its proportions. You can make the suspension soft, but this can result in lots of body roll because of the higher centre of gravity. Or, you can make the suspension stiffer to counteract the body roll, but this will result in a harsh jiggly ride.

We actually have an Ignis, so while I can't compare it to your Qashqai, I can give you an idea what it is like. Seat comfort is pretty good, although due to covid I have not taken it on along journey. Driving position is good, better than the (2017) Jazz we had before it. Interior space is phenomenal for such a small car, four 6' plus adults could fit in quite easily in terms of leg space. It does have a narrow cabin though, something you will be very aware of coming from a Qashqai. On the mid and high spec car, you get 4 seats (*), with two individual rears which slide back and forth about 6", but even with them right back, the boot is a decent enough size for a car that small and certainly big enough for a couple of small terriers, Ride comfort?, I guess a degree of this will come down to expectations and my being being aware of the limitations caused by its proportions, but I think it is perfectly acceptable. As for refinement, again with expectations inline with the type and shape of car, I'm very impressed. At the legal speed limit, while the engine is turning quite high rpm, it is smooth enough not to be intrusive (I have had the car up to 80mph where it was quite happy and not too loud). Performance is surprisingly brisk, it may only have an 89bhp 1.2 but it is a very light car!. £8k is enough to get into a 2018 SZ-T (the top spec) with low miles, like this,

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But you'd really need a god long test drive to find out if it is going to be acceptable.

*The basic SZ3 comes with a (fixed) rear bench seat and three seatbelts, but due to the narrowness of the cabin, there is no way you could fit three adults in there unless very slim!..

Ethan’s suggestion are good but maybe too big? Another smaller one to consider is a Dacia Sandero Stepway. It wouldn’t be among my personal top choices but may meet your size and ground clearance requirements.

I replaced my Quashqai with a Suzuki Vitara. Not sure you will be able to get a 4wd 1.4 turbo within your budget but the 1.6 should be doable.

The OP doesn't want 4x4.

Even easier. Vitara 2wd versions are available and more budget friendly.