MP and head of the influential Treasury Select Committee Nicky Morgan has written to Ms Hogg about the debacle on June 1, which left a number of UK and European cardholders unable to complete transactions.
Ms Hogg is a former Bank of England rate setter, whose brief stint as deputy governor ended last year when she was forced to resign from the role.
Ms Morgan said the incident at Visa led to “widespread inconvenience” for both consumers and businesses.
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She is calling on Visa to give details on when the company and its chief were first aware of the failure.
She has also asked Visa to specify how many cards were ultimately affected and if any customers saw money leave their accounts despite transactions not being completed.
The MP is calling for details over the nature of the hardware failure.