Surcharges have always been added to bills by businesses from airlines to takeaway apps to offset the processing fees charged by credit card companies.
It applies to credit transfers and direct debits as well as online and other payments.
HMRC itself in December said it would stop accepting payments by personal credit cards as a result of the ban, saying: "As a public funded body, HMRC is unable to absorb the cost of personal credit card fees as this would ultimately mean charging the fees back to customers through the public purse".
Treasury minister John Glen said: "Added transparency ensures buyers can make informed choices about how they spend their hard-earned money".
New EU rules come into effect today which will mean customers can't be penalised with extra fees for choosing to pay by credit or debit card.
For example, takeaway firm Just Eat has just replaced its 50p charge for card payments with a 50p "service charge" on all orders.
If you notice any businesses not complying with the ban on credit and debit card surcharges you should report this to Trading Standards Service via Consumerline: 0300 123 6262. However, people will be wary if it results in price increases, minimum spend limits or even cards being refused by retailers.
Previously, retailers had been able to pass on the cost of processing card payments directly to customers in the form of processing fees, but the government has moved to outlaw this practice as it believes it is unfair to consumers.
Some small firms fear the move will add to their costs, and encourage more to accept cash payments only.
However, he added: "With access to cash restricted by a rapidly diminishing bank branch network and threats to ATM funding, small firms now find themselves between a rock and a hard place when it comes to customer payments".
FSB chairman Mike Cherry said: "Removing their freedom to share the burden of card payment fees will give them yet another outgoing to worry about".
But the FSB welcomed today's introduction of "open banking" under which people can let approved third parties other than their own banks - such as price comparison websites - securely access their current accounts, without having to reveal their passwords.