I have never heard anyone pronounce it that way.
What you're looking for is the fact that word-final /ər/ may be lowered to a near-open central unrounded vowel [ɐ] in England, New Zealand and probably in non-rhotic US accents, certainly in AAVE (African American Vernacular English), and to a open central unrounded vowel [ä] in Australia. In other words, LETTER may surface as STRUT.
In North America word-final /ə/ may also be similarly lowered (but I think the most common output is an open-mid central unrounded vowel [ɜ], as that's the most common value of STRUT in USA), also in Afrikaans-influenced Broad South African accents (to a near-open central unrounded vowel), when spelled . Diphthongs /eə̯ ɪə̯ ʊə̯/ may similarly, for some RP (mainly older), Australian and New Zealand English speakers have a lowered second vowel [eɐ̯ ɪɐ̯ ʊɐ̯]. There's a big variation when it comes to these diphthongs, and I'd have to write twice as big message to say enough about them. Just read Wikipedia and you'll get it quickly.
Received Pronunciation examples of lowered word-final /ər/:
employer /ɪmˈplɔɪ̯ə/, [ɪmˈpʰlɔɪ̯ɐ]
water /ˈwɔːtə/, [ˈwɔːtɐ]
better /ˈbetə/, [ˈbetɐ]
Note that first: such lowering is very rare at best (or probably inexistent) when the linking or intrusive /r/ is present, and second: you won't generally encounter lowered LETTER in other positions, unless you're listening to someone from Scotland. As far as I know, in Scottish English there's no phonemic /ər/, as it always merges with /ʌr/ to [ʌr]. But I have a feeling I'm somewhat wrong about Scottish English, so take it with a grain of salt.
General American examples of lowered word-final /ə/:
to (unstressed) /tə/, [tɜ]
the* /ðə/, [ðɜ]
comma /ˈkɑmə/, [ˈkʰɑmɜ]
*The version that doesn't rhyme with "bee".
RP examples of lowered /ə/ in centering diphthongs:
square /ˈskweə̯/, [ˈskweɐ̯]
near /nɪə̯/, [nɪɐ̯]
cure /kjʊə̯/, [kjʊɐ̯]
Bear in mind that even in narrow transcription you'll rarely encounter other symbols than the schwa, for two reasons: it's only a possible pronunciation, and phonemically those are /ər/ and /ə/.
Hope that helped, cheers mate.
I remember being surprised when I first read this that Cruttenden had removed Gimson's comment that this gave the impression to many speakers of being affected. It sounded affected and was rare in 1962 and, in my opinion, this was even more true of 2001- and is of 2013. Upton (2004) described Refined RP as "[o]utmoded and, when heard (typically in old movies and newsreel commentaries) attracting amused comment".
When I wrote in an earlier post, "I have never heard anyone pronounce it that way", I should perhaps have added, "except in old films and in films and television plays in which a certain type of person who is putting on airs is being portrayed."
Cruttenden, Alan (2001.127) Gimson's Pronunciation of English, London: Arnold
Upton, Clive in Kortmann, Bernd and Schneider, Edgar W (eds) (2004.219) A Handbook of Varieties of English (Volume One), Berlin: Mouton de Gruyter.
Yes, it makes much sense, maybe except for a fact that speech of many of the youngest upper class members (including the royal family) often deviates a lot from what's called Mainstream RP (the one taught to ESL students), and sounds like Cockney with no intervocallic glottal stops, no th-fronting and a bit more conservative vowels, maybe a bit less l-vocalization - though I'm not sure of that. Anyway, for these speakers (and like you said, in Refined RP) lowered /ər/ may be more frequent than for anyone else. One may argue though that such people don't speak RP anymore, but the "highest form" of Estuary English. Well, both points of view are valid in my opinion. Maybe it's time to stop using the name RP altogether, as it starts to become somewhat ambiguous and therefore imprecise.
Until someone comes up with a better term that is generally accepted, then I think we may be stuck with RP.
Part of the problem, especially since the BBC became more liberal in its approach to what accents it considered its announcers should have, is that this variety/dialect/accent changes much more quickly than it used to. I suspect that the Daniel Jones who made the term 'Received Pronunciation' well known in the mid 1920s would not have been too surprised by the accent of most BBC announcers in the early 1960s. I am sure he would have regarded mine today, which I generally refer to as RP, as distinctly uneducated - and yet many youngsters I taught (in the south of England!) regarded it as 'posh'. So, even if we come up with a better term, that term is soon going to run into similar problems.
Whatever term we use, many people are, unfortunately, going to regard it as the 'correct' way to speak English.
ps. I've just had an idea. How about 'BECSA' (perhaps pronounced /ˈbeksə/) - British English Coursebook Standard Accent? That would be a moderately accurate description of what it represents, and would automatically remain relevant to the time in which any particular range of coursebooks was popular. It would also perhaps go some way to getting rid of the idea that it was the accent of a group of people in England who spoke the one correct form. Most British publishers of ELT books and audio materials seem to have a fair understanding of what that accent is considered to be. Many of their young employees probably speak it.
That's one funny name. Replace the "c" with "k" and you have a word meaning "crybaby" in Polish. But back on topic, yes, there's a considerable amount of misunderstanding about "British English", "British accent" etc. Especially in USA you can hear people talking about a "British accent" when they really mean an RP or a near-RP variety. Technically this term isn't wrong, as long as you remember it's one of British accents, not the only one. Glaswegian is also British for example, and sounds much closer to German than any southern English variety. I don't mean to offend anyone of course, but that's just the way it objectively is, judging by sounds they use. I personally find it a very original sounding dialect.
Anyway, Standard Southern British (or perhaps "Standard British") sounds very good. For now, if we want to be precise we can just call it "Mainstream RP". People interested in the topic will get the message immediately.