A “small” roof-mount solar panel is about 4 foot by 5. GU10 lamps have different power requirements than strip lights than floodlights than… etc. A big battery is pushing “you might as well do the entire house” territory.
I’m basing this on campervanectrics, but we have a 150W folding panel that’s about 4ft*3ft unfolded. That, when placed in a sunny spot, keeps the leisure battery sufficiently topped up to run a fridge, lighting, radio and phone charging.
So, something similar (panel, controller, battery) would easily be enough to run an LED strip/panel in the shed and a couple of LED spots/floods in the garden. Each of those bits is about (very roughly) £100 though, so you’d be looking at about £500 all in I guess by the time you’d also bought the wiring, some sort of fusebox, lamps/strip etc.