Dismissing criticism of Mr Chavez by human rights groups, Mr Livingstone told BBC Radio 4's Today programme that the President was "the best news out of Latin America in many years". Mr Chavez, said the Mayor, had "brought real democracy and real progress" in Venezuela.
The Venezuelan leader, an admirer of Cuba's Fidel Castro, is on much less cordial terms with Mr Blair, whom he calls "the main ally of Hitler" for his support of President George Bush. During the European Union-Latin America summit in Vienna last week, the Prime Minister warned Mr Chavez and his left-wing Latin American ally, the Bolivian President Evo Morales, to "behave sensibly" as they took more control of their countries' energy sectors.
In previous visits to London, Mr Chavez has met Mr Blair and had an audience with the Queen, but he now regards New Labour economics with disdain. "Neo-liberalism has begun its decline and has come to an end," he said, adding that "a new era has begun in Latin America". The president, a former soldier, has not requested meetings with ministers in London during what Downing Street describes as a private visit. Instead he will meet left-wing Labour MPs and trade union leaders, and speak today at a meeting hosted by Mr Livingstone. The Mayor is also holding a lunch for him tomorrow.
After a turbulent few days in Vienna, at which he and Mr Morales were the centre of attention, Mr Chavez indulged in a final bout of extravagant rhetoric, declaring that America's foreign policy "is as doomed as a pig on its way to the slaughterhouse". Addressing a rally in Vienna with the daughter of the revolutionary Che Guevara, he launched a vitriolic attack on US involvement in Iraq.
"I am sure that this century will see the end of American imperialism," he declared. "For every pig the day arrives for slaughter. For the pig of American imperialism, that time has come."
An icon of the anti-globalisation movement, Mr Chavez's brand of aggressive socialism is taken seriously because of his country's vast oil resources. Ironically, US policy in Iraq has strengthened Mr Chavez's economic position by helping to drive up the price of oil. Enormous Venezuelan reserves, once not worth exploiting, are now destined to be lucrative, and Mr Chavez has taken the opportunity to raise taxes on foreign companies operating in his country. Global nervousness was heightened when Mr Morales, following his mentor's example, announced the nationalisation of Bolivia's energy reserves.
In Vienna only the arrival of a Greenpeace protester and former carnival queen sporting the scantiest of bikinis moved the spotlight briefly from the two Latin American firebrands. As leaders assembled for the "family photo", the protester, Evangelina Carrozo, had to be removed by security. Mr Blair grinned and joked quietly with the Austrian Chancellor and host, Wolfgang Schüssel, that this display was a present from the summit organisers.
The extrovert Venezuelan President gave a more public reaction. "She was very pretty and I blew her a kiss," he said, adding: "It was one of the best things to have happened at this summit." The photo completed, Mr Chavez was engulfed in a media scrum as he launched, from an unscripted defence of Mr Morales, an attack on his political foes.
Mr Morales was, the Venezuelan President said, a direct descendant of an indigenous Latin American people, adding: "These are oppressed people who are rising. They are rising with peace, not weapons. Europe should listen to that."
Mr Chavez added: "There is a big ideological confrontation in the region. Some defend the big project of Washington that has smashed our people. We want a profound change, a new socialism. And we are going to debate: do we want socialism or capitalism? We say socialism!"
Not content with lambasting Mr Bush, he also laid into his Latin American adversaries, including the outgoing Mexican President, Vincente Fox, whom he described as a "puppy dog of imperialism" for promoting a US-backed free-trade area of the Americas. Asked if he would apologise to Mr Fox, Mr Chavez replied "no", before adding that Caracas would wait for a new government in Mexico before attempting to re-establish friendly relations.
Later, hundreds of people crowded into the Vienna Arena to hear him invoking the names of Jesus Christ, Karl Marx, Lenin, Ho Chi Minh, Mao Tse-tung and the Beatles in the cause of global revolution. As she queued for the event, Mira Uebleis, a 17-year-old student, said she had come because Mr Chavez "is going to go down in history".
Other young people seemed less impressed by the Venezuelan leader. As he denounced Mr Bush in terms reminiscent of Mr Castro's four-hour marathons, the crowd was distracted by one couple who engaged in a passionate and public embrace, while others were drifting off to catch the last Metro. The audience assembled for Mr Chavez in London by Mr Livingstone is likely to give him a more respectful hearing.