When two vowel sounds meet, speakers often link them in various ways.
Linking /r/
Some accents of English are described as rhotic, which means that when the letter r appears in the written word after a vowel (as in car or carve), the / r / phoneme is used in the pronunciation of the word (as in /k ɑ: r / and /k ɑ: r v /). Examples are most dialects of American English, Irish English and certain British regional accents. Other accents are non-rhotic, and do not pronounce the / r /, so we get / k ɑ: / and /k ɑ: v /.
RP (Received Pronunciation) is non-rhotic. When, however, there is a written r the end of a word and it occurs between two vowel sounds, speakers with non-rhotic accents often use the phoneme / r / to link the preceding vowel to a following one:
Her English is excellent. (/ r / is pronounced)
Her German is absolutely awful, though! (/ r / is not pronounced)
My brother lives in London. (/ r / is not pronounced)
My brother always phones at the wrong time. (/ r / is pronounced)
Intrusive / r /
Where two vowel sounds meet and there is no written letter r, speakers with non-rhotic accents will still often introduce the / r / phoneme in order to ease the transition. This happens when the first word ends in / ə /, / ɑ: / or / ɔ: /.
Speakers with rhotic accents tend not to do this:
Princess Diana was a victim of media exploitation. / ə r e/
The media are to blame. / ə r ɑ: /
It’s a question of law and order. / ɔ: r ə n /
I saw it happen. / ɔ: r ɪ /
Some speakers also let an / r / intrude within words like drawing (pronouncing it as / d r ɔː r ɪ ŋ / and gnawing / n ɔː r ɪ ŋ /.
Linking / j /
When a word ends in / i: /, or a diphthong which finishes with / ɪ /, speakers often introduce a / j / to ease the transition to a following vowel sound:
I agree, wholeheartedly. /ai ‿ ʲ ‿ ə/
I think, therefore I am. (Descartes) /ai ‿ ʲ ‿ æ/
I am, therefore I ought to be. (G. Kelly) /ai ‿ ʲ ‿ æ/ /ai ‿ ʲ ‿ ɔ:/
They are, aren’t they? (linking /j/, and linking /r/) /ˈðeɪ ‿ ʲ ‿ ɑː r ɑː /
This happens because in order to form / i: / and / ɪ /, the mouth is in more or less the same position as it is for the start of the semi-vowel / j /.