Merging all of the various Government department and agency websites into one was meant to make things easier. As many people have discovered (irrespective of whether they're seeking information about driving licences, passports, tax returns or anything else) it most definitely hasn't!
Any change to (what is currently) an old-style paper licence involves getting a photocard licence. The fee has been increased from £17 to £20, so it's THIS page which is correct:
https://www.gov.uk/exchange-paper-driving-licence