No. That's for people that used to have a UK issued EASA PPL but then changed state before we left EASA, eg to an Irish EASA PPL, & now wish to get a UK PPL on the basis of their EASA PPL.
Your old brown UK PPL is still valid, you just need to renew the SEP rating on it. It always was valid for non-EASA aircraft (eg homebuilts) & now we've left EASA the CAA will allow you to fly what we used to call EASA aircraft but now call Part 21 aircraft on your old UK JAR compliant licence. If you're flying a G-reg SEP around Europe that will be all you need.
If you want to get an EASA licence you can do it at some UK schools:
EASA approved training outside EASA
You will have to get your SEP rating renewed on your old licence first. That will involve some re-training followed by a proficiency check. One new option is the
pilot medical declaration means that you don't need to have a medical to fly G-reg in the UK. If you then want to get an EASA licence you will need an EASA medical as well as the two exams (air law & human performance) & skill test as stated above. It may just be possible to combine the renewal proficiency check & conversion skill test into one test if the examiner holds CAA & EASA ratings.