I would go both sides but unequal to push a bit more west than east.
If you went say 16 panels your around 6.5kw production peak. But you wont see that since your split.
I would go 10 west 6 east so you have a higher load of generation into the evening, when typically people use more.
That should generate you around 4000kwh annually. But 80% will be March-Sept, give or take.
Batteries around 10kwh of storage should see you near enough zero from grid in the Mar-Sept window.
Oct-Feb will be more intermittent you will rely on the batteries more so an off peak tariff may work to charge them up on cheap overnight, best is Octopus go.
You would be looking 16k for a reasonable quote on that, plus a diverter IMO. Less might be possible depending how many installers you try and some luck. Above 16 would be heading into expensive.
Assume another £250 per panel on top of above to cover the panel plus extras needed as your array sizes up.
Don't forget bird netting!