As an Australian and therefore an English speaker who does not pronounce r's at the end of words, I think many rhotic English speakers on this thread - presumably Americans and Canadians - are confusing non-rhotic English pronunciation (ie playa for player) with an inability to pronounce r's (rhotacism).
I am married to a Brit, and have had two decades of exposure to British culture in person and on television, and I have also noticed a prevalence of rhotacism in upper class British media personalities. Prominent examples include Lucy Worsley, Sister Wendy Beckett, and at least three presenters on Antiques Roadshow. All are Oxbidge types, and hence I googled it and here we are.
I know it's anecdotal evidence, but I have never seen this tendency in working class Brits, nore have I seen anyone in American or Australian media with it, except as the butt of a joke. This may be a result of media selection filters, but still. I would be surprised if it wasn't a real thing.