If you want to move house, you may be able to simply port your existing mortgage over to your new property and continue paying it off as usual.
You may have to undergo new affordability and credit checks if you do so and if your new property's value is significantly different from your old one then the situation may get a little more complicated. If you do want to move house, get in touch with your existing mortgage provider first and they'll let you know what options you have at your disposal.