You could try fixing in a mortgage which is portable when you do move - which lots of them are. That way you get the fixed rate for 3,5,10 years.
I remotgaged last year and got a 5-year fixed rate deal through
L&C | The UK's Largest Fee-Free Mortgage Broker and Advisor Despite my general scepticism around financial advisers/brokers they found us a deal i wouldn't have got myself, and I changed my mind several times on what I wanted to do , so I'd recommend them.
Just ring them up, tell the adviser what you want to do, and they should say if its possible or not. It could be that you remotgage on the existing flat in your joint names so you can get a higher mortgage based on joint income.