Mark_C: I can't find the name of the tariffs anywhere on the bills, any ideas ?
It probably says somewhere, but not always exactly the same name as used by the comparison webistes.
No matter, phone your suppler and ask the same question you have asked here. They will likely twig what you are up to and suggest their own better tariff.
Also ask what your annual consumption is in kWhrs, because that gives the most accurate comparison.