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https://www.timefactors.com/collections/smiths/products/smiths-everest-expedition-prs-25
The shop opens for orders periodically, you have to wait and get in quickly. I think you sign up for the newsletter to find out.
Re: mechanical vs quartz, you have to accept that the accuracy will be much worse with a mechanical movement. It will also need periodic servicing at a watchmaker, but probably less frequently than you would have to change a battery. On the other hand, mechanical movements are a lot more interesting, if you like that sort of stuff.
I would tend to assume that a Seiko movement would be quieter and more robust in the long term than a Miyota one. Miyota are one of the cheapest options for a small brand. Swiss movements (eg ETA, Sellita) are unlikely to be found in sub-£500 watches.
Hadn’t thought about it! I do like the idea of not using a battery.
There are so many good suggestions above, I really like all of them, which is a growing problem.
I couldn’t find much on the Smiths Everest Expedition, real mixed search results and some were in the thousands.