Thanks everyone, that's really set me thinking now then... I shall have a look and see what the situation is, because our East-facing roof might be partially sheltered by the neighbour's trees, and the West-facing roof also has dormer windows in, thinking about it! It's just the worst possible shape for solar, basically.
By the way, last night the Powerwall completely discharged itself and stayed at 0% all day. Another phone call to Tesla, and it turns out that you have to set the "sell" price for each rate to be as low as possible. Stupidly, the app copies the "buy" price into the "sell" price field, but leaving it like this stops it charging!! What idiot thought that was a good idea... Anyway, hopefully it will charge overnight now.