Tradesmen are also pretty keen to accept cash these days to avoid VAT too! We phoned only last week to get a shed re-roofed and the guy openly said on the phone that if we paid cash he wouldn't need to add the 20% VAT! That's after we had car repairs last year after an accident when two bodyshops both quoted a "cash without VAT" price, one being £1500! And a bit further back, we had scaffolding put up by a firm that offered to knock off the 20% VAT if we paid in cash and that was £2k! So obviously and these days it's so open! In the past they tended to "suss you out" in person before offering a nudge-nudge discount for cash, but now they offer it freely and openly. Bank charges aren't 20% so it's clearly tax evasion when they knock of such a large amount.
Small shops and takeaways do it too to stay under the £85k VAT threshold as they lose a shed load of money if their declared turnover goes over the £85k - thousands lost, until they grow enough so that there turnover is over, say, £100k which puts them back where they were at £84.5k. So lots manage to stay just under the £85k by not declaring some of their takings. Easy when it's cash, impossible when it's card!!
Money launderers probably DO want people to pay by card as they'll already be putting enough dirty money through the business, so will need an amount of card payments to "balance" it out and look more legitimate if ever investigated as very few businesses will genuinely be cash only these days.
I'd say very few rural shops would want to insist on cash as they're the ones who probably don't have a bank nor post office to pay it in, so will be stuck with potentially large amounts of cash (and having to pay higher insurance premiums to cover it, plus a safe, security alarm, etc) and then more wasted time on a longer journey to take it to the closest bank/PO which could easily be several miles away meaning losing an hour or two! There are even small towns these days without a bank at all and with only a "postal" only post office counter in, say, a convenience store, without banking facilities.
As others have said, bank charges for handling cash can now sometimes be higher than card processing fees, especially with the new, cheaper, competitors such as sumup, lopay, etc. And it's not just bank charges. insurance is expensive to cover cash, both in the premises and in transit, for anything more than trivial amounts of a couple of hundred as petty cash!