I guess the nearest thing we can buy here in terms of price/usefulness/size would be a Jeep Renegade. My wife has one of those and loves it much more than is reasonable. A Duster might work but it just not as cute is it?

Really not very close at all though.

The Jimny is a proper hardcore off-roader, complete with separate chassis and rigid axles, for people who are willing to put up with the compromises that, and its size entails.

The Renegade is none of the above, its just a smallish SUV using the same platform as (amongst others) the Fiat Tipo, but with styling inspired by its more hardcore ancestors. While it is a distinctive looking thing compared to most of its ilk, I personally wouldn't say it was cute, not with that scowling 'face' and jutting 'chin'.

I think there may also be some misunderstanding of just how small a Jimny is. In Japan, the 3 door fits into the Kei car class, that means under 3.4m long and under 1.5m wide. In terms of the actual body structure, there is no difference between theirs and ours. Think about this, have you noticed how narrow a Suzuki Celerio or a Kia Picanto appears?, both are more than 6" wider than the Jimny Kei!. 'Our' Jimny, on paper, was wider than both, but only because of the chunky wheelarches. Yes, the 5 door is longer and has something approaching a boot (with rear seats in place), but make no mistake, it is still a small car (very small to most).

IMO, the car which comes closest to capturing the spirit of the Jimny is the Panda 4x4. And as it happens, its also about as close to the (5 door) Jimny's dimensions as the Renegade.

Over the decades a number of manufacturers have flirted with small proper 4x4s.

The original Fiat Panda from ~1990. Daihatsu Terios from ~1997, Mitsubishi Pinin ~2005. There may be a few more I can't recall.

The UK is not a big market for these despite extraordinary ability off road. The cost of engineering for the low volumes in the UK (Jimny sold 1200 cars in 2019) is high.

In truth, they are for very niche market with serious compromises in comfort, noise, space and performance. They are best suited to those with a real need - eg: living 5+ miles from decent tarmac in Northumberland, Highlands etc. It is just a pose-mobile for urban warriors.

Actually most proper 4x4's started off small.

The original Willy's Jeep was under 3.4m long and under 1.5m wide which, with an appropriate engine size would enable it to be classed as a Kei car in Japan. The original Series 1 Land Rover was almost exactly the same length but just over 1.5m wide. The original Toyota Land Cruiser was give or take the same length and width as a Suzuki Celerio, The original Mitsubishi Shogun/Pajero was about the same length and width as a Honda Jazz (which is also, give or take, the same as the Pinin). The original Daihatsu Fourtrack (FJ20/50) would also be classed as a Kei car barring the engine size.

I could go on but you get the picture!

The Panda 4x4 and Daihatsu Terios were never what I would consider proper 4x4's, with neither having high and low ratio gearboxes. Though both can go a long way off the beaten track thanks to low weight and good ground clearance.