Nigel Lawson may claim that Brexit is finishing the job that Margaret Thatcher started but the prime minister was infuriated by his 1989 resignation, her newly released personal papers reveal.

For the Conservatives, it was a year which had uncanny parallels with today – a prime minister facing questions about her leadership, a party split over Europe and the threat of cabinet resignations over the issue.

Thatcher would survive the year but the resignation of Lawson in October, over the influence of her economic adviser Alan Walters, came, in hindsight, to be seen as the beginning of the end for the Iron Lady.

Lawson was at loggerheads with Thatcher and Walters over the exchange rate mechanism (ERM). The then chancellor was – ironically given his current status as a staunch Brexiter – the only one of the trio who wanted the country to join the ERM, although he was motivated by a desire to control inflation rather than strengthening bonds with Britain’s European partners.

Thatcher recorded his departure in a private memo in terse terms: “Early Thursday morning – hair set 8-8.30 Andrew [Turnbull] came up to say Nigel Lawson wanted to see me. Went down 8.50 …

“The reason for his visit – which he had considered very carefully – was that unless I agreed to sack Alan Walters, he would hand in his resignation as chancellor. This seemed to me an absurd, indeed reprehensible proposition … in my view no one could possibly resign on the basis of such a flimsy and unworthy proposal.”

She said she urged him to think again, concluding: “I then put the matter out of my mind.”

The papers reveal that the following month she told the Sun’s editor at the time, Kelvin MacKenzie, in an off-the-record interview, that after taking a comforting “we love you” call from her children on the day of the resignation, in characteristic no-nonsense fashion she then prepared supper for her and her husband, Denis: “Someone’s got to do it … I just had to get on.”

But Chris Collins, a historian at the Margaret Thatcher Foundation, said the PM’s anger came through in her memo, in contrast with her public stance, in which she affected bafflement. “She would have loved to have really punched hard, I think,” he said.

The resignation prompted the first leadership challenge to Thatcher – by the little-known backbencher Anthony Meyer – which Collins says created the conditions for the epoch-ending contest, less than a year later, in which she would face the more formidable figure of Michael Heseltine.

Collins said: “You can see that events in 1990 would not have happened as they did had it not been for 1989 ... The Lawson resignation is actually the one that makes [Geoffrey] Howe’s resignation so damaging.”

In June of 1989, Howe had teamed up with Lawson for the “Madrid ambush”, when Thatcher’s then chancellor and foreign secretary threatened to resign if she refused to state a date for Britain joining the European exchange rate mechanism (ERM).

She did not accede and although they did not quit immediately, when they did – Howe, then deputy prime minister, resigned in November 1990 – it would ultimately have devastating consequences for her.

Her papers provide an insight into what she thought of the Madrid ambush, with Thatcher writing that two of her aides were “appalled” by the manoeuvrings of her cabinet colleagues.

By contrast to the ERM, Thatcher was a fan of the single market. Little could she have suspected that a “runner” named David Cameron – appearing for the first time in her personal papers in 1989 - writing briefs on the benefits of the single market, would ultimately pave the way for the UK’s possible exit from it.

Other fires Thatcher was fighting in 1989, such as NHS reform and the need to build more houses, also resonate 30 years on, but some, like privatisation, high interest rates and the despised poll tax, were of their time.

Having said that, Thatcher’s determination to plough on with the poll tax, despite grim evidence of its impact, chimes with Theresa May’s steadfast commitment to universal credit in the face of warnings from, among others, John Major, who has likened the two policies to one another.

The papers show she was harangued by backbenchers about the community charge and shown an analysis of its impact on several streets in her constituency, stating that two-person households stood to lose an average of £172 each.

Another confidential report into 10 marginal seats suggested losers would outnumber winners by more than four to one on even the most optimistic assumption.

Faced with numerous troubles, in words that might provide succour to May, the Iron Lady told MacKenzie: “What matters is not the bad days but how you pick yourself up and recover.”

• The papers can be viewed from Monday at Cambridge University’s Churchill Archives Centre and hundreds will go online at www.margaretthatcher.org.

• This article was amended on 9 March 2019 to correct the spelling of Geoffrey Howe’s first name.