"wouldn't explain how they'd arrived at their figures"

More likely couldn't than wouldn't, Eliza. The old days of going into your local Tax Office, talking to a trained Tax Officer, and leaving with a resolution are long gone. Now it's "Compu'aah says no", half-trained call-centre staff who can't answer a question if the answer's not in the list on the the Compu'aah.

Follow Bonzo's advice and put it in writing. But be prepared to wait four months while they get round to opening your letter (that's not a joke, I wrote to them about my wife's and my own tax codes in June 2010, and when I called them in August to ask why I hadn't had a reply, they told me that letters received in June were scheduled to be opened in October.