At least on one point the Israelis and Palestinians agree - we in Europe have lost our nerve. From the Palestinians' envoy to London: "Europe is still an actor in search of a role and we in the Middle East, we have a role in search of an actor. Europe has become too resigned to its marginal role." And this, from Israel's ambassador to the EU: "It is our expectation to see our European democratic friends expressing solidarity and responsibility. It is not working and I am distressed by that."
Why do the European Union and its member states appear so powerless to act? Is it because the other players won't let them? Is it because they can't agree a common foreign policy? Is it our dark history? Is it American muscle? Or is it a lack of will?
The situation is demeaning. Our diplomats shuttle between Brussels and Washington, between Jerusalem and Ramallah, but their efforts are neither noticed nor acted upon. Miguel Moratinos has been the European Union's special representative in the region for the past six years, although you have probably never heard of him. I spoke to him for BBC Radio 4's Analysis programme late last month, in a break between his several meetings.
It had been a particularly distressing day for him. Moratinos had been instrumental in trying to persuade the various Palestinian militia groups to agree to a ceasefire declaration. Just as he was getting close, the Israelis launched an air strike on Gaza, killing a leading member of Hamas and 14 other people, including nine children.
Moratinos claimed that Europe was doing more than it was being credited for. "We are too critical of ourselves," he said. "If we are too soft, we are criticised. When we try to find a way and work with the US we are 'pro-American'."
So what exactly is Europe doing? It is quite active on the ground, engaging with specific disputes such as the Israeli siege of the Church of the Nativity in Bethlehem, which EU diplomats played a major role in helping to settle. But Europe's main function is economic. Over the past decade, the areas covered by the Palestinian Authority have been built up almost entirely with EU money. Now, with the infrastructure all but destroyed, it's our turn again.
"For Brussels, it's not only demoralising, it's a sense of being taken for granted," says Rosemary Hollis, head of the Middle East programme at the Royal Institute of International Affairs. "They are supposed to use European taxpayers' money to build up a Palestinian state in the making, watch it be demolished and then somehow build it up again. How many times do they have to go this route?"
With the Palestinians under curfew, suffering mass unemployment and now malnutrition, it's the job of the Europeans to do the legwork. But Hollis believes our intervention, while well intentioned, could be counter-productive: "In so far as the Europeans are engaged in supplying that emergency aid and keeping the Palestinians just about afloat as a viable entity, they could, in fact, be sustaining an occupation."
Europe as a payer but not a player: what a miserable treadmill we have found ourselves on. It's the Israelis and Americans who call the shots. When ambassador Moratinos and a European delegation tried to see Yasser Arafat in Ramallah during the height of the Israeli incursions into the West Bank in April, they were refused permission. The next day, General Anthony Zinni, the US special envoy, was allowed to go - a calculated snub and a vivid expression of Israeli priorities.
It does not help that Europe struggles to merge the different priorities and historical legacies of the big countries - Britain, France, Germany - into a single policy towards the Middle East. The Israelis believe Europe is using their conflict as a test bed for a common foreign and security policy still in its inception.
Sixty years on, the Holocaust continues to have an impact on the Israeli collective identity - and on the way it deals with Europe. I asked Israel's ambassador in Brussels, Harry Kney-Tal, if European policy-makers, in the light of their history, had a moral obligation to show particular understanding for Israel's position? "I am inclined to answer in the affirmative, yes."
That bind has tightened this year with the re-emergence of individual acts of anti-Semitism in Europe. The American and Israeli right claim that European institutions and mindsets remain locked in pre-war mode. Britain, as ever, tries to have it both ways. It parades its professed proximity to the US administration, while claiming a special role for Europe in peacemaking efforts.
Mike O'Brien, the newly appointed Foreign Office minister with responsibility for the Middle East, makes all the predictable noises about working closely with the US. Part of the job, it seems, is simply to keep the increasingly isolationist Americans at it. "Getting the Americans involved in the peace process is important because they work very closely with the Israelis."
The flip side, logically, is for Europe to deal with the Palestinians. "There are particular individuals who work with the EU who are very well trusted by the Palestinians," O'Brien says. "They can talk directly to the Palestinians in ways that are perhaps easier than for some of the CIA or US personnel."
The trouble is, the Palestinians know who will produce the goods. And it's not us. The Palestinians are as frustrated at our approach as the Israelis are suspicious.
"Europe has enormous economic clout that it has left unused in its relations with Israel," says Afif Safieh, the Palestinian envoy to London. Even though Europe accounts for 70 per cent of Israel's foreign trade, it wouldn't dare use economic pressure. "Europe has been dealt with as though it was a banana republic."
There's the odd resolution in the European Parliament. There's the odd (and controversial) boycott of links with Israeli academics. And then there's that old tactic of governments calling in ambassadors to express concern, as over the recent air attack on Gaza. But although these individual actions antagonise the Israelis, the Palestinians see them as nothing more than going through the motions.
And yet, there is a glimmer of hope. There is a sense that the Israelis and the Americans have begun to listen to Javier Solana, the EU's high representative on foreign affairs. Already, Europe is involved in what is known as the quartet - a new set-up involving the US, the UN, Russia and the EU. The Middle East is Europe's backyard, and with the White House preoccupied with its war on terror, even the Israelis says there is now an opening for Europe.
"Europe is better equipped than the United States," says Kney-Tal. "The Americans sometimes seem to have a lot of impatience with the protracted crisis - they have, you know, a shorter history and they didn't face the problems Europe faces." Europe will have to become not just a payer but a player, he says. It is an intriguing prediction from one of Israel's most senior diplomats. The question is: is it up to the task?
John Kampfner presents Analysis: the expired mandate, BBC Radio 4, 1 August at 8.30pm, repeated 4 August at 9.30pm