Using overdraft to overpay mortgage

My current account has an agreed large overdraft limit. I am thinking about overpaying my mortgage to a degree which will mean that I am overdrawn every month. The idea is that once the mortgage is paid off, I will not be overdrawn and will have cleared my mortgage. The mortgage could be cleared within 12 months.

The problem is that -how much does it cost to be overdrawn on a current account, and whether that is more than the interest on the mortgage.

I don't pay a fine every month on the current account so I think the cost will be in the interest.

Any ideas?
J