If your house is worth £280k, and you have £80k on the mortgage, then you have equity of £200k.
If your divirce settlement required you to split that equity 50/50, you would each get £100k of equity. Your equity would stay in the house. His would be paid to him.
You would therefore remortgage for £180k in your sole name - £80k to cover the existing mortgage, and £100k that you would give to him. That would leave you with your £100k equity tied up in the house.
At the time you remortgage, your conveyancer would tranfer title of the house into your sole name.
However, you need to do that once the divorce settlement has been agreed. That is because you may not be splitting the equity 50/50 if you are offsetting the value of pension assets. So, you need the whole settlement agreed with him before you give him any money at all, otherwise things could get very messy.
Equally, stamp duty will be payable in normal circumstances on the amount you pay to him for transfer of title. However, there is an exemption for transfers made in pursuance of a financial settlement in divorces. So you need the settlement agreed in order to benefit from that exemption.