The Post Office don't actually do ANY basic bank accounts of the type requested.
The Post Office card account (JSA in OK, but only cash out) has a cumbersome application procedure starting with the benefits agency sending you a letter inviting you to apply for one. You then get the form at the PO, fill it in, return it through the PO and eventually pick your card up at te PO. You then several weeks later tell the benefits agency your account details......
The others are not PO accounts at all - just a list of the banks whose basic bank account cards they accept for cash withdrawals. You'd need to look at the web site for each to see if online applications are possible