The origin of it is that the local grocers would also double as the Post Office or where one would receive telegrams. Therefore, "Messages."
It may also have been thought more polite or educated to say, "I'll be going for the messages" than directly referring to buying food, cleaning products and medicines.
Then there's the concept of the shopping list or message, with which somebody, usually a younger member of the household would be sent out, on an errand, to show to the shopkeeper who might be paid, "On tick."
The origin of, "Living on the tick" comes from ticket or tally or tab, not the tick symbol for good or correct.
Then, whilst we're talking about tickets or small, oblong shaped pieces of thin paper, maybe that's why a cigarette is called a tab in the North East?
It's fascinating but complicated.