Interesting feature of some English accents

I'm English (from London), and it was recently pointed out to me by a Swedish friend that when a word that ends in a vowel and a word that begins in a vowel meet, an 'r' sound is inserted to separate them, even though 'r' is not in either word.

For example:
"I know what their agenda is"
"agenda is" gets pronounced as if there were an 'r' on the end of the 'agenda' or on the beginning of the 'is'.

Have any of you noticed this?

We don't use it in the American Midwest.
Maybe its just you Brits.

I'm from New York. I notice that I do that occasionally. My mother does it constantly but she has more of a Boston accent.

I seem to hear that on BBC Radio all the time. Never thought too much of it, though.