I have no idea if this was a fluke or if it might be able to help someone else. Sorry for the weird title which I now realise sounds like a clickbaity advert (doctors can’t believe this one weird trick...)
I had been trying to get a supermarket delivery slot booked and was really surprised when the Morrison’s site offered me a late-night slot the next day, which I booked.
It turned out that our next-door neighbour had an Ocado delivery booked for the same slot. Morrison’s and Ocado share delivery systems and the booking system seems to have been clever enough to offer me a slot when there was a van with space in my road.
Anyway, all of this is to say that if you can text your neighbours and find out if they have deliveries booked you might be able to get a slot for yourself too. The slot appeared about 24 hours before the delivery time.
I really hope that I might have stumbled on something which could help someone else - and if anyone works in logistics I’d be really interested to know if my interpretation of the situation is correct!