Why is it that so many British people pronounce the word “drawing” as “drawring”? This non-standard pronunciation is the result of “overapplication” of a rule governing the pronunciation of most British dialects that says that the final “r” in a word is silent unless it is followed by a vowel.
For instance, the word “roar” is pronounced the same as “raw” in British English, but “roaring” is pronounced raw-ring, since now the “r” is followed by a vowel. The same applies even if the vowel is not part of the same word, e.g. “roar and shout” would be pronounced as “raw-rand-shout”.
When we forget about spelling for a moment, this process is essentially the same as inserting “r” randomly between some words and not between others. As a result, many British speakers started to use “r” as a mere connecting sound between certain pairs of vowels, even when there is no “r” in the written form.
For example, “I saw a man” would be pronounced as “I-saw-ruh-man” and “the idea is” as “the-idea-ris” in many British dialects. Insertion of “r” before a vowel when there is none in spelling is especially common after the long vowel “aw”, probably because most words ending with this vowel do contain an “r”, e.g. “bore”, “core”, “soar”, and after the schwa, that is, the “uh” sound in idea, again because there are many words (minister, matter, later, etc.) that end with it and contain a silent “r”.
This pronunciation is still often considered non-standard (especially when teaching non-native speakers), and most professionally trained speakers, such as news presenters, try to avoid it. Nevertheless, it should not be considered “uneducated” or a sign of the lack of linguistic abilities; from my own experience, I can tell that it is often used even by highly educated people, including university professors, simply because they were born in a region where such a pronunciation is the norm.
Going back to the original question: While the “I-saw-ruh-man” pronunciation should be considered a salient feature of many British dialects (and is generally not discouraged), “drawring” is still frowned upon in professional circles because there is no good reason to put an “r” inside a word that does not contain it.