If the original cost of the bill was �100 or more (before the call-out charge was added) my advice is this:
Start with making a formal complaint to Halifax, Alan. Explain that no such term to make such a charge existed and send them a copy of the agreement.
http://www.halifax.co.uk/contactus/howtocompla in.asp
Then, if they don't recompense you, go to the ombudsman. Their email address is helpfully supplied by Halifax further down the page on the link above.
If the original bill agreed was over �100 the credit card company are joint and severally liable for the supplier having subsequently overcharged you and thus breaching the contract.
Your complaint is on the grounds that Halifax (the creditor) is jointly and severally liable under Section 75 of the Consumer Credit Act 1974, for the supplier's breach of contract. The breach is that you were charged more than you (the debtor) and the hire company (the supplier) had agreed to, and that no agreement existed in which the hirer was permitted to vary the terms of the agreement. Because no agreement to vary the terms existed, the contract cannot be altered unilaterally (Thornton v. Shoe Lane Parking Ltd, 1971).
In addition, since the RAC did not charge the hirer for the call-out, any contractual term that did allow the hirer to charge you is unreasonable and unfair under the terms of the Unfair Contract Terms Act 1977.
That should be enough for the Ombudsman to side with you. If not you can raise a small claims action (costs around �40) against Halifax, the Hire Company, or both. Actually you don't even need to go through the ombudsman to take such action, but it might be less stressful to let the ombudsman get involved. The mere threat of the ombudsman may be enough.