No!
The Post Office card account in the UK is offered by J.P. Morgan and so it would be reasonable to assume you could check it online, but unfortunately this is not yet possible. However, you can check it at ATM machines.
The purpose of the Post Office card account is to be able to receive state pensions, benefits and tax credit payments. It’s the best option if you don’t have a bank account and you’ll be able to take cash out easily. You’ll have a way of collecting your payments too, without having to get the cheques cashed out, which means it’s not as safe as it could be within the confines of a bank account.
Details about the card can be checked out directly from their site here: www2.postoffice.co.uk/counter-services/counter-money-service
You’ll be able to find out the address of your nearest branch with a branch locator located directly on the site. You’ll then be able to conduct business with your Post Office card at the counter or via the ATM cash machine. All you’ll need is your card and your ID password. There is also a customer service number. However they will not give you a total directly over the telephone.
Many people would love to be able to access the account balance online. As a result, it’s important to have your voice heard. If enough people ask for the account information to be made available online, they could easily comply. Until then, it’s counter service or cash machine with the card. If that’s not good enough, then you may want to consider getting a regular bank account and cancelling your Post Office card.