Pointing to an "over-provision" of £900 million in Scotland thanks to an "over-generous" baseline in the UK's funding formula, John Redwood, then the Prime Minister's chief policy adviser who later became Welsh Secretary, even suggested a cut of £500m in the annual £6 billion block grant.
Government documents, released by the National Archives under the 30-year rule, also show that, such was the concern at how much Scotland was receiving in public funds compared with parts of England, an in-depth needs assessment study was proposed by the Treasury but rejected by Mrs Thatcher because of its "real political dangers".
Ever since the Conservatives had taken power in 1979 and sought to bear down on public spending, Scotland's budget had faced cuts threats with George Younger, then Scottish Secretary, fending off the Treasury axe with varying degrees of success.
The papers also reveal that the Thatcher government's determination to remorselessly reduce public expenditure caused friction between the Treasury and other Whitehall departments.
But for 1984 and Scotland it also reveals political intrigue.
Peter Rees, the Chief Secretary to the Treasury, set out the background in a memo to Mrs Thatcher in January 1984, referring to the "substantial over-provision" in Scotland's block grant, that public spending per head north of the border was "30% above England's" and that, because of this and oil production, Scotland was "closing the wealth gap with England".
Mr Redwood suggested Mr Rees and the Prime Minister might "discuss how to broach the subject of the £900m overspend with the Secretary of State for Scotland with a view to opening negotiations, which could result in £0.5bn savings in due course".
In a hand-written note in the margin, Mrs Thatcher seemed unimpressed: "I do not think they will get us very far. But we can have a short meeting."
Nonetheless, the Treasury still pressed for cuts and a needs assessment study but Andrew Turnbull, the PM's Private Secretary, raised the Scottish Secretary's "strong reservations".
"If it were to show that Scotland was under-provided for, the Government would lose a major plank in its defence against Scottish Nationalism. If this study showed Scotland were over-provided for, it would be inevitable that the Treasury would seek to cut this back, which would create a major political issue in Scotland," he wrote.
Mr Turnbull stressed how Mrs Thatcher had come out against such a study, fearing it presented "real political dangers".
He said she felt "it would be better...to trim Scottish programmes as and when opportunity arose rather than through a very conspicuous exercise".
Mr Turnbull said cuts had to be handled with "great care". "There should be no attempt to publicise the figures. Instead, the aim should be to pare them down."
He feared a "frontal assault" on public expenditure in Scotland "could create a possible opening for the SNP" and ended his note: "I would be grateful if this letter were shown only to those who need to know of its content."
Under pressure from the Treasury, Mr Younger had agreed the Scottish block be cut by £5m in 1985/6, £5m in 1986/7 and £20m in 1987/8; a total of £30m.
But in November 1984, Mr Rees told Mr Younger he had to find an extra £36m in cuts for 1985/6. But the Chief Secretary made clear the block grant total for that year in the Public Expenditure White Paper would be unchanged from that previously announced in the Autumn Statement, "so minimising the risk that these adjustments will be 'visible'".
In a note to Mr Rees, Mr Younger said he was "astonished" to learn of the request for a sevenfold increase in just one year. Mr Rees reduced his proposed cut for 1985/6 to £20m, meaning the total requested reduction over three years was £60m, double what Mr Younger had offered.
In a letter in December 1984, Mr Younger made clear he was willing to "trim my programme by whatever figure I judged could be guaranteed to remain invisible to my critics in these matters". His proposed £30m cut over three years was, he insisted, the "most I could surrender without risk of detection".
Mr Younger said: "I am simply not prepared to run the acute political risks of cutting my programme further by an arbitrary amount, which I would be unable to explain or defend."
But the Chief Secretary told him he was not the only Secretary of State asked "to make highly unwelcome sacrifices".
Mr Rees then pointed out how the complexity of the comparability programme between Scottish and English spending and the fact that it was "nowhere published" meant he did "not find it easy to accept that a £20m shortfall will be impossible to disguise or defend".
Mr Younger replied that the Treasury was making an "unjustified attempt to take resources from me" and the extra £15m it was seeking in 1985/6 was "based on no rational grounds or even on a calculation of invisibility".
But Mr Rees stood his ground.
Lord Whitelaw, who chaired the spending committee, conceded defeat and said no further savings could be found quickly beyond those offered by Mr Younger but that full discussions on the "problem of visibility" should take place to find greater savings in future.
A spokesman for First Minister Alex Salmond said: "These are astonishing revelations. Not only did Mrs Thatcher conspire to cut Scotland's grant, she made sure the plan was kept secret from Scottish voters."
He went on: "Unfortunately, things have not changed all that much.
"Today's Tories are ganging up with the other Westminster parties to scrap the Barnett Formula and replace it with a system which would reduce the money available to the Scottish Government by £4bn a year."