Hello, I am Keith, one of the experts on Just Answer, and pleased to be able to help you with your question.
Interest at 60K seems a trifle steep. Is this an accurate figure on the interest due on the debt or merely one based on assumptions. HMRC are very keen to make assumptions, invariably incorrect and always in the Revenue's favour.
By acting as you have already done and asking for chapter and verse regarding their demands. HMRC tend to take a long time to respond to correspondence these days.
Just keep plugging away at them. Also tell them that you are appealing against their actions. This freezes the whole affair until agreement is reached.