Gaza is a secular society where people listen to pop music, watch TV and many women walk the streets unveiled

Last week I was in Gaza. While I was there I met a group of 20 or so police officers who were undergoing a course in conflict management. They were eager to know whether foreigners felt safer since Hamas had taken over the Government? Indeed we did, we told them. Without doubt the past 18 months had seen a comparative calm on the streets of Gaza; no gunmen on the streets, no more kidnappings. They smiled with great pride and waved us goodbye.

Less than a week later all of these men were dead, killed by an Israeli rocket at a graduation ceremony. Were they "dangerous Hamas militant gunmen"? No, they were unarmed police officers, public servants killed not in a "militant training camp" but in the same police station in the middle of Gaza City that had been used by the British, the Israelis and Fatah during their periods of rule there.

This distinction is crucial because while the horrific scenes in Gaza and Israel play themselves out on our television screens, a war of words is being fought that is clouding our understanding of the realities on the ground.

Who or what is Hamas, the movement that Ehud Barak, the Israeli Defence Minister, would like to wipe out as though it were a virus? Why did it win the Palestinian elections and why does it allow rockets to be fired into Israel? The story of Hamas over the past three years reveals how the Israeli, US and UK governments' misunderstanding of this Islamist movement has led us to the brutal and desperate situation that we are in now.

The story begins nearly three years ago when Change and Reform - Hamas's political party - unexpectedly won the first free and fair elections in the Arab world, on a platform of ending endemic corruption and improving the almost non-existent public services in Gaza and the West Bank. Against a divided opposition this ostensibly religious party impressed the predominantly secular community to win with 42 per cent of the vote.

Palestinians did not vote for Hamas because it was dedicated to the destruction of the state of Israel or because it had been responsible for waves of suicide bombings that had killed Israeli citizens. They voted for Hamas because they thought that Fatah, the party of the rejected Government, had failed them. Despite renouncing violence and recognising the state of Israel Fatah had not achieved a Palestinian state. It is crucial to know this to understand the supposed rejectionist position of Hamas. It won't recognise Israel or renounce the right to resist until it is sure of the world's commitment to a just solution to the Palestinian issue.

In the five years that I have been visiting Gaza and the West Bank, I have met hundreds of Hamas politicians and supporters. None of them has professed the goal of Islamising Palestinian society, Taleban-style. Hamas relies on secular voters too much to do that. People still listen to pop music, watch television and women still choose whether to wear the veil or not.

The political leadership of Hamas is probably the most highly qualified in the world. Boasting more than 500 PhDs in its ranks, the majority are middle-class professionals - doctors, dentists, scientists and engineers. Most of its leadership have been educated in our universities and harbour no ideological hatred towards the West. It is a grievance-based movement, dedicated to addressing the injustice done to its people. It has consistently offered a ten-year ceasefire to give breathing space to resolve a conflict that has continued for more than 60 years.

The Bush-Blair response to the Hamas victory in 2006 is the key to today's horror. Instead of accepting the democratically elected Government, they funded an attempt to remove it by force; training and arming groups of Fatah fighters to unseat Hamas militarily and impose a new, unelected government on the Palestinians. Further, 45 Hamas MPs are still being held in Israeli jails.

Six months ago the Israeli Government agreed to an Egyptian- brokered ceasefire with Hamas. In return for a ceasefire, Israel agreed to open the crossing points and allow a free flow of essential supplies in and out of Gaza. The rocket barrages ended but the crossings never fully opened, and the people of Gaza began to starve. This crippling embargo was no reward for peace.

When Westerners ask what is in the mind of Hamas leaders when they order or allow rockets to be fired at Israel they fail to understand the Palestinian position. Two months ago the Israeli Defence Forces broke the ceasefire by entering Gaza and beginning the cycle of killing again. In the Palestinian narrative each round of rocket attacks is a response to Israeli attacks. In the Israeli narrative it is the other way round.

But what does it mean when Mr Barak talks of destroying Hamas? Does it mean killing the 42 per cent of Palestinians who voted for it? Does it mean reoccupying the Gaza strip that Israel withdrew from so painfully three years ago? Or does it mean permanently separating the Palestinians of Gaza and the West Bank, politically and geographically? And for those whose mantra is Israeli security, what sort of threat do the three quarters of a million young people growing up in Gaza with an implacable hatred of those who starve and bomb them pose?

It is said that this conflict is impossible to solve. In fact, it is very simple. The top 1,000 people who run Israel - the politicians, generals and security staff - and the top Palestinian Islamists have never met. Genuine peace will require that these two groups sit down together without preconditions. But the events of the past few days seem to have made this more unlikely than ever. That is the challenge for the new administration in Washington and for its European allies.

William Sieghart is chairman of Forward Thinking, an independent conflict resolution agency