Notwithstanding with that, what they're trying to do to me looks like a cheeky breach of the fixed term contract we already have and common contract law in general. You might argue that paragraph 3.1 of the terms allows the increase ("We may vary our charges from time to time") but I can tell you the clause if perfectly void in context of a fixed term plan. Although business grounds behind the increase can be valid, as a customer I do not have to care; those grounds cannot change the legal requirement to obey the existing fixed term contract.
I agree with you. Although following my comment earlier in this thread we did, ashamedly, decide that this is a fight we simply can't be bothered with right now. Last time I had to fight with Slingshot's helpdesk resulted in months of stress involving three faulty ADSL modems and a requirement for me to spend large amounts of time building detailed evidence of the faults of two of them (I gave up trying with the third), but that's another story.
We will, however, be considering shopping around to see what alternatives are available once our fixed term runs out.