City car that can cope with countryside: steep hills, mud and bumpy rocky roads (high undercarriage)

[DrinkFeckArseGirls]

My daughter and I live in London so we need a fairly small car. if we want to park anywhere. However we do travel to Cornwall, Somerset, Wales and need a car that can cope with the countryside roads. Our current small city car cannot deal with this (we had to stop up a steep hill 2 days back and make a 3-point turn to go back down - revving in gear one was not making that car go any higher.
A day before that we could hear the undercarriage scratching as we went up a very steep and very rocky driveway (if you can call it that - just a path up a steep hill)!
The current car can take a while to get up to speed so turning into all those national limit country roads is occasionally interesting - it takes a while to get up to 60.
I'm thinking a small SUV with a more powerful engine that a current 1.2 ltr? What would you recommend. It will have to be second hand.

Bump. I’m thinking Skoda Yeti but it’s a long car.

Ah, it sounds like you need my modest dream car the Daihatsu Terios. I live rurally so don't have the city bit to deal with but I've fallen in love with the Terios as the only small 4x4 I could ever afford to run. Fingers crossed for in about two years for me.

The Terios offers all the punch of a full size 4x4 with the agility of a small sports hatch. High driving position and expert handling make this car the perfect transition from off-road to on-road.

Fiat Panda Cross?
NOT the new City Cross though

A Jeep Wrangler would fit the bill,

Friends have a Skoda Yetti, it’s their second, and they love it’s practically. Skoda have stopped production so you might get a second hand bargain. They’re 4.22 m long so it’s pretty average for that type of small SUV.
I was tempted myself and took one for a test drive, it was great, but something else caught my eye.

I live in London so we need a fairly small car.

A Jeep Wrangler would fit the bill

Fucking hell! If that's a small car in your book, what do you drive, a stretch Hummer?

What about a Mini Countryman? Or some sort of mini with a higher clearance?

Vitara ( Ideally DieseL) Or Suzuki jiminy lesser ride quality but unstoppable in the lanes, just consider a slightly more aggressive tyre and you should have no issues

VW - T Roc is compact. Expensive though.