From Wikipedia's page on Indian English
A number of distinctive features of Indian English are due to "the vagaries of English spelling". Most Indian languages, unlike English, have a nearly phonetic spelling, so the spelling of a word is a highly reliable guide to its modern pronunciation. Indians' tendency to pronounce English phonetically as well can cause divergence from Western English.
In RP [Received Pronunciation], /r/ occurs only before a vowel. But some speakers of Indian English, primarily in the South, use /r/ in almost all positions in words using the letter 'r', similar to most American and some Irish dialects. The allophone used is a mild trill or a tap. Indian speakers do not typically use the retroflex approximant /ɻ/ for , which is common for American English speakers
This feature, I'm surmising, is mainly based on the socioeconomic status of the Indian English speaker and whether they studied in the British Isles or in the US.
The period of highest migration from India to England was between 1955 and 1975. Post-war Britain found itself in the midst of a severe shortage of labour and in 1948 the British Nationality Act was issued, this granted Commonwealth citizens free entry to Britain.
In India, the majority of families who took advantage of this law were from middle-ranking peasant families in Punjab, whose fathers, brothers and husbands had previously been employed in the colonial army or the police force. Their children attended British state schools and many acquired or “learnt” the British accent. In the following audio excerpt, Gilli Salvat remembers arriving in England from India shortly after 1948 and her experience attending school. Throughout the excerpt, she speaks with a marked London accent with no trace of rhoticity whatsoever. Towards the end of the recording she says,
(2.04) And when I went to school, all the kids, equally used to take the piss out of me. Right? Because of how I talked and they thought that I was an Indian from the States. Yeah? Like, a red Indian. Right? And, er, I think in about three weeks I changed my accent and, um, I started learning to survive.
Instead, the wealthy generally chose to remain in India and during the 1950s, 60s, and 70s a number of them sent their children abroad to English boarding or grammar schools and/or universities. As a result, highly educated English speaking Indians did not sound like the stereotypical Indians that used to be mocked, mimicked or parodied by the British from that era.
Wikipedia confirms my limited experience–I used to live in London during the 70s and early 80s–and says
While there is an assumption that English is readily available in India, available studies show that its usage is actually restricted to the elite, because of inadequate education to large parts of the Indian population. The use of outdated teaching methods and the poor grasp of English exhibited by the authors of many guidebooks, disadvantage students who rely on these books.
From the website eslan (English Speak Like a Native)
In Hindi, the [r] has the same quality as the /t̬/ (the tap) in English. The tongue tip quickly taps the alveolar ridge. … The British /r/ on the other hand is always silent at the end of the words and between a vowel and a consonant. E.g road; cord; park; ordinary; letter; first etc.
Indian learners often do pronounce the silent /r/.
In an essay shared by Darshan Kadu, four main features of Indian English are listed, the rhotic /r/ is never mentioned but the third feature probably explains why the speech of many Indian English speakers has the rhotic /r/
3. Indians, quite often, tend to speak English with the same accent they use for their mother tongue. Since there are several regions and regional languages, the English spoken by Indians gets influenced by their native accents.
That is why the English accent of a person from Kerala is quite different from that of Tamil Nadu or West Bengal or Punjab. Not only gets the accent, the pronunciation of English words also influenced by regional factors.
There is a YouTube video of an Indian woman, which seems to have been lifted from a dating site, who is clearly not a British or an American speaker. The title of the clip is Indian English–Pronunciation–rhotic r, and she speaks with a thick Indian accent and rolls her Rs. I only wish I could identify which region she is from but I simply haven't got a clue.
Do as many wealthy Indian families send their children to English boarding and prep schools, and/or to universities as they did back in the 1900s-1970s?
…India's strong history with British boarding schools stretching back over a hundred years.
Unfortunately, I don't know the answer to that question but I would wager that US universities attract far greater numbers of Indians and Pakistanis than thirty or forty years ago. Secondly, and lastly, educated Indians who did not spend their childhood in England, but immigrated to the British Isles during the 50s, 60s, and 70s often spoke excellent English but their sometimes thick accents and idiosyncratic word stress made it easy to identify them as immigrants from British Indians who were born and grew up in the UK.
General Indian English and its myriads of other English dialects (e.g. Malayali English, Maharashtrian English, Punjabi English, Bengali English, Hindi English) is a fascinating topic which I know very little of but on EL&U we do have many IE speakers whom I sure could explain far better and in far greater detail and depth.