LINKING R
In BrE a final -R is silent, because it is not followed by a vowel, so TEACHER is pronounced /ti:tʃə/.
But if that word is followed by another word that begins with a vowel, then the R is followed by a vowel and so, it is pronounced:
He's the new teacher of maths 
now, the final -R in TEACHER is pronounced
"teacherofmaths": /hi:z ðə nju: ti:tʃər əv mæθs/
This final R that joins one word with the next is called a "linking R".
INTRUSIVE R
In Brititsh English, words ending in R sometimes pronounce it (linking R) and sometimes don't pronounce it.
From a native's point of view, there are words that end in a vowel but when the next word begins with a vowel they use an / r / to join both words. Then, it is only natural that sometimes they use a "linking R" in the wrong place. We call that an "intrusive R", and it happens a lot in BrE.
A book about Africa and America many British people will pronounce this "africarandamerica"
