Hello!
I can't believe I've been motivated by this to get a copy of Hugo Young's One of Us, which I read over 30 years ago.
Some useful extracts for your questions:
'[Alfred Roberts] was a small businessman on the way up. Choice not necessity led him to make his family take baths in an unplumbed tub for the first twenty years of Margaret's life: the muscular meanness of a man who positively frowned on the smallest form of self-indulgence...
'The Roberts [Margaret] knew belonged to the rising petty bourgeoisie not the beleaguered working class. In the mid-1930s, according to a historian, 75 per cent of all families were officially designated as working-class, earning £4 weekly or less... Alfred was already among the 20 per cent who could call themselves, if they chose, middle-class. As a shopkeeper, indeed, he was a particularly powerful member of it' (p.21).
It's interesting to note that the Conservative Party agent in Grantham thought Roberts likely to be right-wing Labour, who stood as an Independent - since formal affiliation didn't matter so much in local politics at the time. Roberts may also have been put off by the Cooperative Party controlling Labour in Grantham, which provided competition with his own shops (p.22).
Through local politics, family were also connected to Lord Brownlow, the head of the local landowning family who was also a municipal servant. When Thatcher reached No. 10, the family loaned Margaret the family silver to dignify the public rooms in Downing Street (p.24).
Margaret won a county scholarship to KGGS, which meant that the half of the fees her parents would normally have paid were covered (p.26). Young describes her as: 'not particularly brilliant, but she was very hard-working, and her contemporaries remember her as a model pupil of demure habits and tediously impeccable behaviour' (p.26).
He notes that KGGS, typical for girls' day schools at the time, had 'a thin but steady stream of pupils passing on to Oxford and Cambridge' (p.28). And '[Roberts] managed to put together the money to send her, since she was not awarded a scholarship' (p.30).
Young's conclusion is that 'after considering her early life as Alfred's adored creation, one is obliged to revise the common belief that her entry to Oxford was remarkable' (p.31).
The key hurdle was the entry to KGGS, I think - winning the county scholarship certainly helped, but she would have attended anyway, with the money saved from not having indoor plumbing and relentless hard work.
Four-fifths of children left school at 14 in the late 1930s and early 1940s. So the talent pool was much smaller. Moreover, the girls' schools at the time were extremely strong - partly because so many of their teachers became career teachers after the First World War.
It is hard to say how a candidate of Thatcher's ability would fare nowadays. The diligence and seriousness would play extremely well at interview if a girl of that calibre got to the interviewing stage. It's not really a thought experiment that makes sense: the nonconformists of Thatcher's generation often headed towards London and the professions, rather than staying in small businesses.
So if we imagine that MT hadn't been born, but that her double had been born in 2007 as Alf Roberts' great-granddaughter - it's much more likely she would have grown up in a well-positioned family in London's commuter belt, attending one of the better-known private day schools or super-selective grammar schools, depending on whether her parents had worked in the private or public sector. If the family had stayed in Grantham, KGGS still has a reliable handful of students heading to Oxbridge each year.
But it's hard to imagine that that young person, growing up in the 2000s, would have been brought up with such strict Methodism and discipline, or in 'a home of aggressive thrift' (p.29). And that discipline plus her good-but-not-brilliant brain helped her get to Somerville - admittedly the strongest of the women's colleges in academic terms. (Of course, all of the women's colleges were academically-strong - because there were so few of them, and they had the pick of female applicants.)
I'll leave it to Oxford to explain that their offer rates to state school candidates are very much not 'artificially supported by policies that seek to recruit young people who attended state run schools'.
@Blossomtoes and @Efacsen - university fees were still payable until 1962 following the recommendations of the Anderson Report, which is why scholarships still mattered so much: University fees in historical perspective - History & Policy