Ronald Reagan is back. Today more than a thousand people crowded into London's Grosvenor Square to celebrate the centenary of the birth of the former US president. The ceremony, held a few metres from the US embassy, saw the unveiling of a 10ft bronze statue of Reagan, who died in 2004 at 93.

A hundred years on from his birth, seven from his death, and 22 years after he left the Oval Office, the Gipper remains a towering figure in American politics. In recent weeks Republican presidential candidates have been falling over each other to invoke his name and wrap themselves in his mantle, as Bushes I and II are quietly airbrushed from the party's history. Even Barack Obama, after his "shellacking" in November's midterm elections, made it known to reporters that he was reading a biography of Reagan. Oh, and liberal icon John Lennon was, according to his assistant, a secret supporter of America's 40th president.

But which Reagan is being commemorated? The man or the myth? Conservatives, and especially neoconservatives, have deified him as the warrior president who won the cold war with a combination of a muscular foreign policy and a well-funded military. Progressives have dismissed him as a cowboy president, hellbent on confrontation with the Soviet Union and itching to nuke Moscow. (His humorous asides didn't help: on one occasion Reagan leaned into a microphone and joked: "My fellow Americans, I'm pleased to tell you today that I've signed legislation that will outlaw Russia forever. We begin bombing in five minutes.")

But have both his supporters and his critics got him wrong? Neoconservatives, for instance, have long claimed that they are his ideological heirs. One of the most influential neocon texts, a 1996 essay in the journal Foreign Affairs by William Kristol and Robert Kagan, was titled "Toward a Neo-Reaganite Foreign Policy". The following year, in its founding "statement of principles", the now notorious neocon Project for the New American Century called for a "Reaganite policy of military strength and moral clarity".

The coalition's own neocon-in-chief – the education secretary, Michael Gove – writing in 2004, claimed that "it was because Ronald Reagan kept the faith that he achieved so much. What was that faith? In a word, neoconservatism."

It is a bogus claim. Reagan was no neocon. Unchallenged by progressives, rightwing hawks have rewritten history, leaving neocons like Kristol and Gove free to appropriate his name for their own belligerent ends.

Don't get me wrong. Reagan was no peacenik, either. A card-carrying cold warrior, he secretly sold weapons to Iran and Iraq, illegally funded the Nicaraguan Contras, provided aid to a Guatemalan army later accused by a UN-backed truth commission of carrying out "acts of genocide", and supported Osama bin Laden's mujahideen in Afghanistan, and Jonas Savimbi's Unita in Angola.

Nonetheless, he succeeded in avoiding a direct military confrontation. As the liberal US writer Peter Beinart argues in his book, The Icarus Syndrome: A History of American Hubris: "On the ultimate test of hawkdom – the willingness to send US troops into harm's way – Reagan was no bird of prey. He launched exactly one land war, against Grenada, whose army totalled 600 men. It lasted two days. And his only air war – the 1986 bombing of Libya – was even briefer."

In contrast, consider the blood-spattered record of his successors. George Bush launched Gulf war I and sent troops into Panama and Somalia; Bill Clinton bombed Iraq, Sudan, Afghanistan and Yugoslavia; George W Bush invaded Afghanistan and gave us Gulf war II and the war on terror. And the Nobel peace prize winner Obama had troops surging in Afghanistan, launched a war on Libya and sent drones into Yemen, Somalia and Pakistan.

Lest we forget, after America's first encounter with jihadist violence in 1983 – when 241 US military personnel were killed – Reagan, to use the disparaging lingo of the neocons, chose to "cut and run". Every single soldier was pulled out of Lebanon within four months. "Perhaps we didn't appreciate fully enough the depth of the hatred and the complexity of the problems that made the Middle East such a jungle," Reagan later wrote in his memoir, adding: "The irrationality of Middle Eastern politics forced us to rethink our policy there … If that policy had changed towards more of a neutral position ... those 241 marines would be alive today."

These are the words not of a hawk but of a dove; of a leader who did not share the neocons' blind faith in the use of military force to spread freedom.

The truth is that Reagan wasn't a Reaganite; he ended the cold war through negotiation and with far fewer military interventions than his successors have managed so far in the war on terror. His actions, rather than his occasionally bombastic words, reveal a president more interested in jaw-jaw than war-war.

A quote from Margaret Thatcher on the plinth of his statue in London reads: "Ronald Reagan won the cold war without firing a shot." There is an important lesson in those words for today's hawkish, gun-toting conservatives.

• The standfirst on this article was corrected on 5 July 2011. It originally stated that the anniversary of Reagan's birth fell this week. In fact it occurred in February