No, the rate on your mortgage is fixed for two or five years — after that, you’ll go onto a floating rate. At which point you should remortgage into another fixed rate, but enough people suffer from inertia that they don’t.
I hear people getting on the housing ladder today are generally getting 30 year mortgages.
Translating that into some of the more expensive areas of the US, that payment would be extreme requiring two low 6-figure earners.