Yes you can, subject to the terms and conditions of your current mortgage deal, which you will find in your mortgage offer/variation agreement document - this is known as 'Porting'.
You will effectively be applying for a new mortgage on the new property, but would be taking the current interest rate/deal from your current mortgage with you. You can find out more on our page for existing mortgage customers moving home.
Your home may be repossessed if you do not keep up repayments on your mortgage