It's not quite as easy using the value increase of the property though. I planned on doing this in my last house but the bank won't just apply average price increases and accept that as the value (or even specific local house price increases) I would have needed to pay for an official valuation of the house. Then there's the risk that if the valuation isn't enough to get you into the next 5% band it won't help your rate at all and you've just wasted a few hundred for the valuation.
In the end it worked out that I was quite close to moving down a band but the price increase wouldn't have been enough to take me into the next band below that so I could just overpay a bit extra from my savings and didn't look much more into a valuation.