Please refer to this short extract:
5.—(1) A contractual term which has not been individually negotiated shall be regarded as unfair if, contrary to the requirement of good faith, it causes a significant imbalance in the parties' rights and obligations arising under the contract, to the detriment of the consumer.
(2) A term shall always be regarded as not having been individually negotiated where it has been drafted in advance and the consumer has therefore not been able to influence the substance of the term.
(3) Notwithstanding that a specific term or certain aspects of it in a contract has been individually negotiated, these Regulations shall apply to the rest of a contract if an overall assessment of it indicates that it is a pre-formulated standard contract.
(4) It shall be for any seller or supplier who claims that a term was individually negotiated to show that it was.
(5) Schedule 2 to these Regulations contains an indicative and non-exhaustive list of the terms which may be regarded as unfair.
You made two assertions.
The first was that there is a legal right to cancel a BT contract any time before their price increases take effect irrespective of the 10-day limit prescribed in the T&C. That implies a specific legal provision (as opposed to unfairness), which does not appear in the legislation you quote.
The second was that unfair T&C can be challenged in court. The quoted legislation does indeed require a contract to be fair, but proving that it's not is a challenge beyond the average customer and a delight for the legal profession. On the face of it the mobile phone minimum-period contracts are less fair than BT's in that they allow no cancellation on the grounds of price increases at all, let alone with a time limit. Yet, despite their distaste, all Ofcom can do is launch a consultation while Which? have resorted to a campaign.
That's all some distance from the easy options you indicated in your first post.
This thread relates to the price increases in January this year, not the ones for January 2014, which are on a totally different thread.
This thread appears to have been accidentally hijacked, so I have moved the post to the correct thread, which discusses the increases next year.