Margaret Thatcher believed that Menachem Begin was the "most difficult" man she had to deal with in the early years of her premiership, and thought his West Bank policy "absurd".
The former Prime Minister's views about her Israeli counterpart are unearthed in documents released by the National Archives under the 30-year rule.
The previously secret papers reveal that, during a tête-à-tête with President Giscard of France at Number 10 in November 1979, Mrs Thatcher discussed how she had "never had a more difficult man to deal with" than Mr Begin.
President Giscard said he had "always been surprised at the degree of support which the Labour government had given Israel".
However he did admit that he understood the emotional reasons for the support, and felt the same situation applied to France because of the size of her Jewish community. The archives reveal President Giscard "did not know Mr Begin, whom he had never met, but he thought his approach fanatical and unrealistic".
Mrs Thatcher responded by saying she "agreed entirely with what President Giscard had said about Mr Begin".
She added: "All our efforts to convince Mr Begin that his West Bank policy was absurd, and that there should not be Israeli settlements on the West Bank, had failed to move him."
Mrs Thatcher told President Giscard that, although Britain was ready to talk to representatives of the Palestinian people, recognition of the PLO would have to be accompanied by the PLO's acceptance of Israel's right to exist.
Many of the released documents, covering the period from September 1979 to the end of 1980, consider the reverberations from Israel's historic Camp David Accords peace treaty with Egypt in 1978.
One source of discussion was the possibility of a full-scale conflict between Israel and the Palestinians, with John Robinson, the British ambassador to Israel (who stayed in post for a very short time) , offering a chilling warning of what might come. In a secret note to London in May 1980, he wrote: "It is now clear…the Camp David negotiations will not lead to a comprehensive agreement. No agreement on the West Bank and Jerusalem is possible."
He predicted that if it came to war, Israel "will be ready to use their atomic weapon. Because they cannot sustain a long war, they would have to use it early".
The suitability of engaging the PLO in talks brought much hand-wringing from the British.
Lord Hailsham wrote to Mrs Thatcher, who was the MP for Finchley and Golders Green, North London, warning of the potential for disastrous consequences if talks took place with Yasir Arafat's organisation.
"We should not underestimate the importance of Jewish opinion here. It is fanatically involved in the fate of Israel. Even non-observant or non-Zionist Jews take this stance. Manchester, Leeds and the whole of north London would be profoundly affected. Have we not enough on our plate just now not to consider leaving this hot potato alone?"
On April 3 the Prime Minister wrote to Kenneth Baker, later Home Secretary: "There is no change in our policy towards recognition of the PLO, nor do we accept their claim to be the sole legitimate representative of the Palestinians.
"We do however accept that the PLO is an important factor in the area and that at some stage they will have to be associated with negotiations."
She said the government continually encouraged the PLO to renounce terrorism and no settlement would be possible until it agreed to such principles.
"Please assure your constituents that our commitment to Israel's future is in no way diminished," she added.