So there seems to be a difference of opinion on when stock (if available) shows. Below is my approach, but it may be completely wrong (and I just got lucky with people returning / cancelling at a timepoints).
I assume that stock only shows when the physical delivery is checked into the store. So I was checking around 0930 onwards (using the available pickup in the checkout on the Apple site). In my case, around 1000 they showed the 256GB/Natural as being available in Norwich (and was for about 1hr). I also saw some available devices in Battersea for a couple of minutes and also Edinburgh.
I have 3 sets of postcodes (I live in Cambridge and don't mind a train ride to a store anywhere that's a few hours away) that I use working on the assumption that availability is via shipment from China that hits lots of stores in the UK on the same day:
WC2E 8HB (the Apple Covent Garden store) so this looks at all the London stores
NR2 1SU (the Norwich Store) that gives wider area North of London
G1 2JX (the Glasgow Store, an idea of pipeline if any are available).
As noted, another poster says stock opens at 0600 so it may be that I just got lucky !! The approach above has worked over the years to the point where even though there is a store in Cambridge, I've bought about 75% of my store reserved iPhone and Watch in Norwichwithin about 1 week of release.