"...near the bottom of the page was a note that says they will claim £15 a month from my account",
That's because you agreed to their terms and conditions when you accepted the cashback offer.
There have been many complaints about this scheme over the past seven or eight years, but some time ago Webloyalty said that its offer page and banner have been reviewed by the Committee of Advertising Practice and it has confirmed that both comply with the British Code of Advertising, Sales Promotion and Direct Marketing.
I'm afraid this is a salutary lesson to read the small print when you accept any kind of offer. You may be entering into an agreement.