Depending on the contract you signed they may be within their rights to automatically renew it at a higher premium. If you cancel the payment route you may be the one that ends up in the wrong side of a courtroom and possibly blacklisted. On the other hand if their contract is such that it infringes on certain legal rights it may not be worth the paper it's written on.
Well said that man. Do not just cancel the payment method or it will just spiral into debt collection.
I studied law for a while and my immediate thoughts are :-
1. Lord Denning's 'Red Hand Rule' may apply. Basically means that if a contract term is unexpected and/or has serious impact, for the term to be binding it should be clearly pointed out to you (e.g. a red hand marked next to it pointing to it, though that's just an example). A contract that upped the fees sevenfold in the second year might very well meet that, meaning burying it in small print made it non-binding. But I've a feeling that what happened may be that they told you upfront what the annual fees were but gave you a whopping discount in the first year...am I right? That might not give a strong case. In any case you're reliant there on the judge's opinion on whether it's a 'Big Red Hand' matter or not and therefore not all that cut and dried. So it's not the greatest option in law in practical terms.
2. Unfair Terms In Consumer Contract Regs 1999 (UTCCR 1999). This legislation lays out a raft of terms in contracts entered into by consumers which are deemed unfair and unenforceable, because the contract places disproportionate cost or burden onto the consumer. It's a pretty short and digestible bit of legislation (no, really) and I suggest you have a look, at sections 5 to 8 which explain what it is, and Schedule 2 which is a bumper fun list of examples of unfair, unenforceable terms - examples 1h and 1l look potentially relevant in your case. However it pretty much needs to be a standard contract of theirs that you signed, not anything individually negotiated :-
The Unfair Terms in Consumer Contracts Regulations 1999
3. There's also The Consumer Protection from Unfair Trading Regulations 2008 which I don't know much about and don't think helps you here, although boy do the Schedule 1 examples make interesting reading for anyone who doesn't like being diddled :-
The Consumer Protection from Unfair Trading Regulations 2008
So, how best to proceed...you could tell them that you have taken legal advice [ don't say it was me

] based on which you believe the arrangement is unenforceable under UTCCR 1999, and also the price increase contravenes Lord Denning's Red Hand Rule as articulated in Spurling v Bradshaw 1956; you therefore intend to raise a case on this basis with the Financial Ombudsman Service (FOS); you may also notify both the Office Of The Director Of Fair Trading and your local Trading Standards requiring them to pursue a breach of UTCCR 1999, Schedule 2, paragraphs 1h and 1l; they should be aware that FOS or OFT ruling against them will set a precedent where they have to apply the ruling to ALL such contracts with ALL their customers; and you intend to do all of this with absolute maximum publicity and fanfare, including to local and national press, the This Is Money pages and website of the Daily Mail, the Motley Fool website, moneysavingexpert.com, and others as you may deem appropriate. However, if they agree to cancel the contract on a goodwill basis with no further moneys to be taken, none of the above will happen and you will let the matter rest.
If they tell you to shove it, the Financial Ombudsman Service is probably a good first port of call. Simple form to be filled out and no cost to you. However all they do in essence is review the contract terms and compliance with them, not whether the contract holds water in law. They're not lawyers. And/or try local Trading Standards.
I am not a lawyer and it is your own responsibility if you take any of the above advice.
By the way, anyone who feels like slagging off the EU and its interference with this country, I don't necessarily disagree with you entirely, but note that the 1999 and 2008 rules are something we had to implement (to protect the consumer against scumbag companies) because it was an EU requirement.