Finance experts Payment Sense said at 6.30pm the problem is slowly being fixed and some cards have begun to work again. Contactless payments are the most likely method of card payment to get through.
A Visa spokesman said the problem is not related to customers' cards or accounts, but that there is a glitch in the authorisation process on the merchant's side.
A Transport for London spokesperson has confirmed that people will still be able to use affected cards to travel on the capital's buses, trains, Tubes, DLR and Overground services.
"Customers using contactless payment cards should be able to carry on using our Tube, bus and rail services as normal," they said.
"We are monitoring the situation in close collaboration with our payments providers."
Some social media users saw a lighter side to the disruption today, joking about cards being declined in famously inexpensive stores such as Primark and speculating about the response of the Queen, who is said to never carry cash.
Banks Barclays, Santander, HSBC, Natwest and Lloyds Bank told customers they are working to resolve the outage as soon as possible on Twitter.
Until then people are advised to carry alternative forms of payment to Visa.
High street banks have told customers that the problem is being resolved slowly. The disruption follows a three-day outage at Visa's settlement system last year.