Nothing to add to BigMac, but I will anyway.
As mentioned the major banks don't tend to give interest at any significant level on current accounts, the adverts are specific in their claims saying they offer 60 x more than Barclays, Lloyds standard current accounts, this is true, as you say they can't claim something if it was not.
This is not to say these banks do not offer other rates just that their standard rates are that low, as in fact I'm sure Halifax also offer accounts which such low rates. It should also be mentioned that these high rate current accounts are generally a load of rubbish anyway because the rules to actually get you the 3/6% rates are fairly tight, a certain limit on how much you must put in each month and how high a balance you must maintain, for many people they would never get such high rates of interest.