This is what's known as an intrusive-R.

Many dialects of English (for example, British) are non-rhotic, which means that the letter R after a vowel is not pronounced. So whereas an American speaker would say "hard" with a clear "R", a British speaker would say it similar to "hahd" or "hawd".

When a word ending with a vowel is followed by another word starting with a vowel, it can sound a bit clumsy having two consecutive vowels, which is why in English and other languages, a consonant is inserted, for example, instead of "a apple", we use the word "an" which serves to insert a consonant: "an apple"

In such case, if the first word ends with a non-rhotic R (which comes out as vowel sound), a speaker of non-rhotic English will insert a consonant sound by pronouncing the otherwise silent R. So whereas a British speaker would normally pronounce "car" as "cah", the phrase "car at…" would come out as "car at" with a pronounced R.

If you get used to inserting an R in certain cases, such as "car at", it becomes so natural that at times you will do it even if the first word doesn't end with an R, but sounds like the kind of word that would. So "saw a film" becomes "sawr a film", and eventually, even if it's not followed by an vowel, you might end up saying "sawr".