It's a toughie, that's for sure. especially here in the Uk, where benefits are NOT distributed at the start of the calender month, but rather at four-weekly intervals; and exactly when is individually determined so far as i know.
I don't think that priority for folk on benefits as such exists. It's just priority for "vulnerable"" people. There's a big overlap between those two groups ofc, but also a lot of folk whose dependancy on benefits is not linked with any particular vulnerabilty, eg low-paid workers claiming top-up benefits. But I don't think any of those people will find themselves able to wait for a food delivery, They're generally living hand-to-mouth and will need to get straight out to the shops as soon as the money rolls into the bank.
During the past few weeks, i've seen things move from a position where next daydeliveries were commomly available, to fully booked up for the next three weeks. Ocado have got the wait-time down to one week, mostly (so far as I can see) by means of cancelling all orders that fall ouside that timespan (including two of mine) and making people hover over their computers on the off-chance that a new slot has now been freed up , together with the smaller off-chance that they're amongst the lucky few who spotted it first.
That said, hats off to Ocado. They've done a remarkable job of coping with ten times as many customers as usual, far as I can see . I just much preferred having to book my deliveries two to three weeks in advance to their present ploy, which introduces way too much uncertainty.