Hello, I am Keith, one of the experts on Just Answer, and pleased to be able to help you with your question.
Adding your wife - yes you can, but better leave a decent interval, say a few months. Even HMRC recommend this tax avoidance. Doing so will divide your profit in half, 22.5K less your non cumulative Annual Exempt Amounts (AEA) of 11.1K, each exposed to CGT at 28%, tax bill say 3.2K each.
If your bank is holding the deeds as the lender than you will have to get their approval to the transaction to which they may not agree. In any event a lender might charge a hefty fee for the privilege.
I do hope that you have found my reply of assistance and hope I have not rained too hard on your parade.
Delighted to have been of assistance.
Thank you for your excellent support.
No why should they? Your problem will be getting the bank to change the existing mortgage terms at all.