We were shopping online for years before COVID arrived.
Since everyone else has been competing for not enough delivery slots we have mainly switched to Click and Collect. It is a great alternative .
We shop with Tescos and they have had a big sign on the website requesting that we all think twice before taking a slot that an extremely vulnerable person could use instead - hence us using Click and Collect.
So basically yes, the delivery slots can be found, especially if you wait up til midnight and are willing to queue for a slot that is 3 weeks in advance, but I'm happy with Click and Collect. You can have more than one shop booked at a time, so you can set them up weekly, if you want.
My parents are Sainsbury’s shoppers (again, online shopping set up a year ago). They are on the Vulnerable List and can usually get a slot with 1-3 days notice. No idea how it works for Sainsbury’s non ExtremelyVulnerables.
Oh, and a friend of the family has rung the Waitrose customer services, and been added to the priority list, as an over 70, so she now gets deliveries too.