Hi
I understand your point and from your comments it sounds like you were on a nil service charge tariff.
Generally, these are billed in a suppliers system as the first 1145kwh or whatever per quarter are billed on the higher rate and any other usage after that amount is billed on the lower price. It will probably be explained that way in their standard T&C's which should be available on their website or on request.
Most likely the billing system they use will simply not take into account change of supply situations in these calculations and this is why this has happened. You could argue it, and you might get £30 out of it (1000 units at 3p diff between prices, however i'm unsure of their prices and you might want to check that on your bill).
Strictly speaking, there are no regulations on suppliers regarding how this type of tariff is billed so they dont really have to give you it, they may do as goodwill, but are under no obligation to do so.
If you did want to take it further i'd visit their website, look for their complaint handling statement or procedures, and write. "I'll get the billing department to look at that" is actually call centre code for "I'll tell you what you want to hear, get you off the phone, and do nothing"