Leo Abse was one of the sons of Rudolf Abse, a Jewish solicitor and cinema owner who lived in Cardiff. One of Abse's grandfathers was from Poland, and the his grandmother from Germany.8. Abse's younger brother Dannie Abse is a well-known poet; their older brother Wilfred Abse (1915-2005) was an eminent psychoanalyst. Abse attended Howard Gardens High School in Cardiff and then the London School of Economics, where he studied law. Having joined the Labour Party in 1934, he clandestinely visited Spain during the closing months of the Spanish Civil War, in 1939.

Leo was married 1955 to Marjorie Davies who died 1996. They had children Tobias and Bathsheba. He married second 2000 Ania Czepulkowska when he was 83 and she was 33. He left his £1.2m estate to Ania, disinheriting his children and grandchildren.

During the Second World War Abse served in the Royal Air Force. He was in Cairo in 1944 when some of the British military personnel stationed there set up a "Forces Parliament" in which they debated the structure of society they wanted to see in the post-war world. Abse's idealistic left-wing views were fully in tune with the majority opinion among the lower ranks at its meetings, but the existence of the "Parliament" disturbed the senior officers. When Abse moved a motion supporting nationalization of the Bank of England he was arrested and the Forces Parliament was forcibly dissolved.

After the end of the war Abse set up in practice as a solicitor in Cardiff. In 1951 he established his own law firm, Leo Abse & Cohen, which eventually grew to be the biggest in the city. He was also elected as Chairman of Cardiff Labour Party for two years from 1951, giving up the post when he was elected to Cardiff City Council. Abse fought the then-safe Conservative seat of Cardiff North in the 1955 general election, but was defeated.

Daniel Granville West, the Labour MP for Pontypool and, like Abse, a solicitor, was awarded one of the first life peerages in 1958. Unusually for a town in the South Wales valleys at that time, the National Union of Mineworkers was not in control of the nomination of West's successor as Labour candidate, since Pontypool was a centre of the railway industry. Abse won the candidacy and then won the seat at the by-election.

In the House of Commons Abse swiftly acquired a reputation for independence of spirit. He made a point of dressing flamboyantly on Budget day, and liked to drop references from Freudian psychotherapy into his speeches. Although his abilities might have taken him to high office, Abse remained a backbench MP. This factor, together with the fact that he had a safe seat, freed him from the restrictions that prevented most other MPs from taking up controversial subjects.

In 1963 Abse was selected in third place in the ballot for Private Member's Bills and introduced the Matrimonial Causes Bill, which simplified and made easier the legal process of divorce.

In 1957 the Wolfenden Report had recommended that the law be changed to legalise consenting male homosexual sex, but the government had taken no action. Abse began to promote a Bill to put Wolfenden's recommendations into law in February 1962. He kept pressing the issue and, after Humphry Berkeley (Conservative MP for Lancaster) lost his seat in the 1966 general election, Abse became the main sponsor for the legalisation. Although with the Labour landslide of 1966 there was a majority for the Bill, it was still vulnerable but Abse persuaded Roy Jenkins to give the measure government time, which eventually saw the Bill through onto the statute book.

Abse's views on homosexuality were strongly influenced by his knowledge of psychotherapy. He argued that an obsession with the question of punishment of homosexuals "has hitherto prompted us to avoid the real challenge of preventing little boys from growing up to be adult homosexuals. Surely, what we should be preoccupied with is the question of how we can, if it is possible, reduce the number of faulty males in the community". Abse put his arguments in this way partly to ensure that those MPs who were inclined to vote for the Bill did not feel they were endangering their masculinity but mostly because he had a view that "those who do not procreate are deprived or stunted" (the analysis of Antony Grey, who was leading the lobbying efforts of the Homosexual Law Reform Society and worked closely with him).

During the Six Day War in 1967 Abse made a passionate attack on those Labour MPs who had supported the Arab cause. In 1968 he was appointed to a Home Office advisory committee on the penal system. He was elected Chairman of the group of Welsh Labour MPs in 1971.

In 1973 Abse requested that the government ban the rock singer Alice Cooper and his group from performing in England, claiming that Alice was "peddling the culture of the concentration camp". Abse claimed: "Pop is one thing, anthems of necrophilia are quite another".

Abse was chosen to be Chairman of a select committee on abortion from 1975 to 1977. His report advocated restrictions on abortion, including a lowering of the time limit within which abortion was legal from 28 weeks. He fought in the House of Commons for the enactment of his committee's recommendations, and continued the fight in 1980 when the Conservative MP John Corrie proposed a Bill along similar lines: Abse refused to compromise on a limit of 24 weeks.

Abse was an opponent of devolution when it was proposed in the late 1970s. He also proposed a separate referendum on whether the Shetland Islands ought to be part of a devolved Scotland. Abse was briefly Chairman of the Welsh Affairs Select Committee when it was first set up, but resigned in November 1981. One of the reasons why he opposed devolution was that he thought some in Wales, whom he called "fanatics", wanted to use it to promote the use of the Welsh language. He opposed in particular proposals for criminal juries comprising only Welsh speakers, and described Welsh-language television as an "expensive farce" and a "gravy train".

Abse added to his reputation for taking maverick stances by strongly urging that British forces be withdrawn from Northern Ireland. He opposed nuclear power and nuclear weapons, and criticised Margaret Thatcher for insisting that Argentina unconditionally surrender over the Falkland Islands. However, he supported British membership of the European Communities. His support for liberal divorce laws led him to propose a new 'child-centred' divorce reform in the early 1980s; the Bill was piloted by Martin Stevens, Conservative MP for Fulham.

Abse was elected for the renamed seat of Torfaen in 1983, but retired from Parliament in 1987. The first of the books he then wrote, Margaret, Daughter of Beatrice (1989), is a "psycho-biography" of Margaret Thatcher, taking its title from the observation that while Mrs Thatcher frequently referred to her father, she claimed not to have had anything to say to her mother from the age of 15.

In Wotan, My Enemy (1994) Abse took a psychoanalytic approach to explaining the origin of British hostility to Germany and the idea of the European Union. In The Man behind the Smile: Tony Blair and the Politics of Perversion (1996) Abse highlighted some of the aspects of Tony Blair's that were later to be cited by Blair's opponents on the left. A revised edition, Tony Blair: The Man who Lost His Smile (2003), was published in the United States). In this edition Abse took the opportunity to claim that he had paid off a blackmailer who had been targeting a fellow Welsh MP George Thomas (Speaker of the House of Commons from 1976 to 1983), on the basis of Thomas's (closeted) homosexuality.

Finally, in Fellatio, Masochism, Politics and Love (1997) Abse drew attention to the fact that fellatio had been unspoken of a generation before but had since come to be seen as an essential part of casual sexual relationships. He analysed the tendency for men to engage in risky behaviour by placing their trust in women whom they barely know and linked it to political developments. The book was published in the United States in 2000 shortly after the scandal of Bill Clinton's relationship with Monica Lewinsky had been revealed.

A bust of Abse was unveiled at the National Museum of Wales in Cardiff on 22 October 2009. The sculpture was funded by the firm of solicitors he founded, Leo Abse and Cohen, and was made by Abse's second cousin, Luke Shepherd.