How far is too far?

I'm planning on a few long UK weekends away this year, using our Jimny to get there and back.

It's a 2008 auto that's covered 76k, serviced within last year.

We will be using A & B roads as I don't fancy motorways in a 1.3 with only 4 gears.

How far can I drive in one go before taking a break to give the engine a rest?

Until you run out of fuel.  This is why engines took over from horses.

With Jimnys the car will rust out quicker than the engine breaking down lol. In all seriousness it will be you needing a break before the car needs one. I would expect a Jimny to happily drive around the UK without the car needing anything.

The last few years I have been doing long trips with my 2005 Jimny mostly pulling a 350-450kg trailer and with all I need to sustain myself and tools and parts and firewood and camping gear. Well loaded.
Driving mostly bad gravel roads, mountain passes in Norway up to 1400m and down and back up again. Clutch have been smelly for years
Servicing has been so so but mostly ok.
Most of these trips is over a week or two, approx 2500km thru Denmark, Sweden. I try not to do long hauls but to see the sites and take it slow and easy exploring. Also going to offroad events so not exactly being nice to the car either. Using it for what it was built for.
Some days though I can do longer hauls with 8 to 10 hours of driving. not so many km's as these roads is very hard to get more than 60kmh average speed on but have reached 600km in one day sometimes.

As long as your brakes are good and serviced, tyres good, check the oil, fluid levels and cooling, there is no reason you could not drive all day.
The engine is the least of my worries.
My car has been modified a bit so I worry more for the drive train.
If your car is original there should be no worries.

I routinely drive the North Coast 500 in my auto which given where I live means a round trip of at least 1600 miles depending on which way I go. This usually takes me between 3 or 4 days though I have done it several times in 2 days. The limiting factor is how much fuel you are prepared to carry because you are guaranteed to use the tank up before you find a fuel station at least once so having a contingency helps keep the schedule in check. Oh and motorway driving with the auto is much better as 4th is really long and the revs are manageable on the ears compared with the manual.. really it depends on how much you like driving because the jimny just eats the miles.

Oh and for reference I see distance the same way Australian and American people do, an hour and a half for a bag of chips for tea is entirely reasonable.