If you pay by a credit or debit card in one of the stores, belonging to large chains like Sainsbury's, Tesco and so on, you can see on their receipts a disclaimer, stating something like "2.5% of total due is paid to Big-Name Cards Processing Ltd. to cover the transaction costs. This does not affect the total amount paid by you".
I always marvelled at the generosity of the chain owners, who, faced with such hefty card handling fees, chose not to pass them on to the consumer, but rather to suffer the loss. But lately it was brough to my attention, that there was actually a nice tax trick, exploited by the companies - the 17.5% VAT does not apply to the transaction costs, so if you pay £100 in cash, there will be £14.89 due to Her Majesty in VAT, but when you pay by card, there will be only £14.52 to pay (if I still remember my math).
So, for every £100 they save around £0.37, which doesn't seem a lot, until you think about their daily sales volumes. I think in reality their transaction costs for handling credit card payments are much smaller than 2.5% of the total - they are big enough to bargain a good discounts from major card operators. Also, by not handling cash, they reduce expenses related to fraud, theft and robbery (and insurance through it) and physical handling of real money. So it is probably quite profitable to them to accept plastic, especially since the introduction of Pin and Chip, which reduced card fraud to some extend.
An unrelated story is told by BBC. According to the article, there is a rise in VAT fraud in the UK. Usually the scheme is quite simple - goods are imported and sold, the price including the VAT, but the collected tax is never paid to HMRC. Some are even more sophisticated - they import and export the same goods time after time, reclaiming the VAT when they export and, as said before, not paying it when they bring it back.