Why should he pay. As an unmarried couple they get none of the financial benefits to being married such as the removal of CGT between each other. So why should he cover her debts?
In fact, since they are unmarried, any gift he gave her to pay off her tax bill would probably be subject to CGT meaning he would be paying an additional 28% to clear her debt.
He's worth 10 million and wouldn't have missed it. Not even with an extra 28%.