Barclays and Halifax both suffered problems with their online banking systems on Monday.
Barclays customers reported encountering messages such as: "Barclays Online Banking is currently unavailable" and "the server is too busy to respond to your request" when trying to log into their accounts.
A message on the Barclays website currently reads: "We're currently experiencing technical problems in Online Banking that mean some of you may not be able to log in to the service.
"We apologise for any inconvenience this may cause and suggest you try logging in again later," the message continues.
Similarly, many Halifax customers said that they were unable to log in to their accounts in order to make payments or transfer money.
However, a statement on the Halifax website said that its online banking service was now operating normally.
It was suggested that the sheer weight of numbers of people trying to access their accounts on the first working day of 2010 could have caused problems for the sites.
However, a spokesman for the Payments Council, the organisation that sets strategy for UK payments said that online banking sites "should all be set up to deal with large levels of users so capacity issues shouldn't be a reason".