I do not think so. Otherwise the British government would not have needed to outlaw charging customers more for card transactions to encourage the move away from cash.
Alternatively, they were counting the time they spent cash handling as a business owner as zero cost, which isn’t really true.
Someone willing to take the risk of the severe penalties for dodging taxes would not be deterred from offering discounts for cash payments because they broke another law by doing so. They can also avoid the law by not taking card payments at all. I have found that many people in businesses traditionally took cash payments do not take cards but are happy to be paid by bank transfer (which is usually free on both sides in the UK if the sender is not a business).
The value of the time spent on cash handling may be very low. What is the opportunity cost of the time if it can be done in otherwise dead time? It is worth what value they attach to it.
Most small places not declaring cash want to stay off the radar, they use tricks like using old cash resisters that don't have trackable invoice ids.
Food places are rife with it as they can claim excess food was thrown out as spoiled.