You really don't need to go into that much detail, a single mid size panel 50-75watt, and a circa 15-20 watt 12V LED light panel, or chain of panels, a battery and simple PWM solar controller is all you need. You could probably get by with a smaller panel, but why bother with todays prices.
Something like:
and a small deep cycle battery which you might be best off buying locally, or something like this U1 battery commonly used in electric scooters
You could probably shave $30+ off that price with a bit of shopping, I found similar light kits without the wiring and the switch for 1/3 the price, what it comes down to is a 25 watt panel would probably be plenty for this, but why not overkill when a 25 watt panel is $59 and a 50 watt is $79 with mounting brackets, solar controller, wires, etc.
p.s. here is another contender panel that is $5 more, but includes more wire, including battery clips
https://smile.amazon.com/dp/B0956TH7Q8 the UK has a reputation for being cloudy, which is another reason to oversize things.