There are some things which will be taken to account though. You will be given "credit" for all your payments that you have made towards the mortgage.
My husband went to court with his ex over the house and this is what happend. Just say the equity in the house is worth �20,000, you would be entitled to 50% each, so �10,000 each. But any payment you have made would be taken into account, so say you paid �10,000 in payments, this would drop the equity in the house to �10,000, so it would be �5,000 each.
Obviously I cannot guarantee this would happen but it did in my husbands case. His ex was given half credits towards the payments on the mortgage. If you have made the payments for the last 12 years it would dramatically reduce the amount of equity and the amount your ex could claim.
You need to see a solicitor, but you never know, your ex may not want to go down this route and could be happy to have her name taken off the mortgage.