The visa outage seems to be by no means uniform, and other stores across the shopping precinct reported no problems at all this afternoon.
The issue affects Visa credit card holders who are trying to pay for items or withdraw cash from ATMs.
Responding to The News" Facebook page, Tarah Puxty said: "Asda Gosport have been affected and their cash machines are empty. "Not knowing when this is going to be sorted out is incredibly frustrating".
A Visa statement said: 'Visa is now experiencing a service disruption.
The extent and of the problem, which Visa called a "service disruption", has not yet been clarified by Visa.
A United Kingdom wide payment issue is affecting local businesses this afternoon.
The market for global payment cards is dominated by China's UnionPay, Visa, and Mastercard, according to research and consulting firm RBR (pdf).
Responding to customer complaints on social media, HSBC said there were issues with processing Visa payments, which were intermittent, but were "slowly recovering". Can you advise on best route to resolution as this is causing me serious problems. "Bloody nuisance", said another Twitter user.
Image: Shops quickly filled up as customers had issues paying with Visa cards.
Elle Gibbs-Murray, from Bridgend, said she was stuck in traffic on the Severn Bridge for 45 minutes as drivers were unable to pay the toll by card.