Yes, that’s wrong. Many people have used cheaper (tens of pounds) or free (like mine) deeds poll in order to change their name. However, note that you will have to pay to renew your passport (currently between £46 and £85.50), as normal, and while you’ll be credited with extra lifespan on it if your old one hasn’t expired yet, this caps out at 9 months, so if your existing passport has more than 9 months left on it then you will end up losing out slightly. However, the deed poll itself is free.