In that time people had no access to their money, no tap and pay, chip and pin etc, nothing.
That was quite a lesson in importance of cash, another lesson was about a dozen years ago when all the banks here went to the wall and had to be nationalised in order prevent bank runs.
Pubs were local guides to credit worthiness, larger shops cashed cheques so businesses could pay staff (an era when many were still paid in cash), so cash could go round the system again, and cheques were countersigned and passed on dozens and dozens of times -- effectively becoming variable size bank notes.
It's a fascinating story, and quite remarkable how little effect no banking had.
Doesn't sound like there was "no harm to the economy" though, except in the broader sense. A quote from an Irish building contractor cited in the article: "I employ only 10 people. If it hadn’t been for the bank strike I’d be hiring 30. I’d say I’ve lost up to £20,000 over it ... One of my problems is finding the money to pay the wages. I run round from Wednesday to Friday to scrape them up, and in that time I can do no other work."
The article also notes the steady stream of people going down to the local department store and other larger shops once a week, to cash their wages, or a wages cheque to pay their factory workers. Pubs were accumulating cashed cheques from regulars and some making smaller loans.
The real surprise for me is how smoothly they coped, and how little fall out there seemed to be when banks reopened. Though of course there were some of the millions of cheques doing the rounds that did bounce. I've seen far less about knock on effects after reopening like that, but it's usually described in a way that makes it seem "far less than you would expect".
PS OP, in the 1700s you'd probably issue a writ of payment and the shopkeeper would add the purchase to your tab, which you'd pay off in full at a later date.
Unless you were a total stranger to that establishment, then you'd probably be paying at the time of purchase.
Let's get our jokes historical accurate.
All seriousness aside, if a business wants to be cashless, that’s a business decision, not religion. If the system goes down, they can dogmatically refuse to function, or they can place a large can on the counter and get on with it.
By the way this highlights the need for something like Bitcoin.