Do british people pronounce the letter r if its followed by a vowel?

Im trying to learn the standard british accent(aka rp) because it sounds fabulous and its non rhotic(pronouncing the r in english makes me sound unnatural sometimes) so i came across this rule that says you must use a linking r if a word is followed by a vowel sound

For instance:

Fair enough,for example,car engine...

Nonetheless when i listen to british people they dont seem to use this rule

Can someone elaborate?