Well, I think because there were possibly lives of British citizens at stake, according to Irene. It could have been a lie, but I don't think Mycroft was willing to take that chance.
But in what sense could that have been true?
If the phone contained information that would have saved their lives, would Irene have divulged it? We saw no evidence whatsoever of any public-spiritedness on her part. She was out for herself, pure and simple -- not saying there's anything wrong with that, just that she's clearly not the sort of person you'd want to rely on for help.
If, on the other hand, the phone contained information that would have put their lives in danger -- well, then, just as well to destroy it, right?