Fawzia al-Kurd's home is nothing special. She has lived within its walls for the past quarter of a century, in the heart of East Jerusalem's Sheikh Jarrah district. The house is tidy. But at first glance, it would not appear to be worth $10m.

That is the sum that the al-Kurd family claim they were offered by Israeli buyers as an incentive to move on, a figure confirmed by their lawyer. Fawzia refused to make a deal, whatever the price. It would have hurt her 'integrity' to take it and leave, she said. So last week she received an eviction notice, based on an arcane legal claim to the site that her husband first called home in 1956.

If she and her family are forced to leave as a result, ultra-Orthodox Israeli settlers from a company called Nahlat Shemoun - linked to a nearby Jewish shrine - will take over half of the house. Settlers have already occupied her illegally built extension. The Kurd house may soon be draped with Israeli flags - as is another a handful of metres distant - and Arab East Jerusalem will have shrunk perceptibly once more.

'Their objective [in trying to evict me] is political', said Fawzia. 'They are claiming as theirs something that is not.'

The story of Fawzia's house reflects the larger battle for the future of Jerusalem, a city contested with an intensity and urgency unmatched anywhere else in the world. In the interminable saga of the Middle East peace process, agreement on the 'final status' of the Holy City remains as elusive as ever.

As Fawzia pondered her eviction notice, Gordon Brown arrived in town to tell the Knesset that he favoured Jerusalem as a shared capital of two separate states: Israeli and Palestinian. US presidential hopeful Barack Obama followed, and adroitly back-tracked on a recent assertion that the city, as the capital of Israel, 'must remain undivided'. 'Final status,' he said, would be for the 'two sides to negotiate'.

What is at issue now is what has been at stake since Israel's foundation and before: how can two peoples' claim on a city as the centre of their national ambitions ever be reconciled? Since the 'uniting' of Jerusalem in the Six Day War of 1967, when Israeli troops overran Jordanian positions on the east side of the city, Palestinians have largely watched, furious but impotent, as Israeli construction in Arab East Jerusalem has proceeded apace. Israeli flags dotted around Palestinian quarters bear defiant testimony to Jewish insistence on a unified city and capital.

And despite the evidence that some now in Israeli politics, not least Vice-President Haim Ramon, would like to see the city shared, with special arrangements made for the so-called Holy Basin at its heart - home to the major shrines - the 'facts on the ground' point to a concerted Jewish expansion into the Palestinian east of the city.

Small settlements - like those encroaching on Sheikh Jarrah and other neighbourhoods - have set their sights on the east's strategic points, a series of stepping-stones linking Jewish West Jerusalem via East Jerusalem with the Old City. Larger ones such as Har Homa and Ma'ale Adumim have expanded as ever-growing buffers which hem in the Arab neighbourhoods, linking the Israeli settlements ever closer to the centre.

All that is left for Arab Jerusalemites is resistance in the Israeli courts, the dream of a capital and the hope that frightens Israelis most - that their increasing demographic advantage will save the city for them in the long run.

'Final status' notwithstanding, the city is divided already - psychologically, culturally and politically. There is the Jewish west of the city with its vast hinterland of malls and cafes and street musicians. There is the beleaguered Arab quarter of the Old City, where large families cram into improbably small apartments. And there are places where the two sides do meet - like the Mamilla Mall just outside the Old City's Jaffa Gate, where wealthier Palestinians mingle, under the pavement umbrellas, sipping orange juice and black coffee with secular and religious Jews - and among the apartment blocks up on French Hill near the Hebrew University.

In recent months Jewish West Jerusalem has been forced to re-examine its assumptions about its Arab neighbours - which it had believed posed considerably less threat than those living on the West Bank - after three attacks launched by residents living in the city's east, all of them apparently unrelated to organised militant groups.

There was a 'copycat' attack last week in which a resident of East Jerusalem went on the rampage with a bulldozer on the eve of Obama's visit, leaving two Israelis injured and the driver shot dead by a settler. A similar incident earlier this month made headlines around the world and led to calls for a security crackdown in the east of the city.

In the immediate aftermath of last week's attack, one elderly Jew at the scene asked anyone who would listen whether it was not time to 'screen' Arab employees of the municipality more carefully.

The comments follow the revelation last week that in the first six months of this year 71 Palestinian residents of East Jerusalem had been arrested on terrorism charges, double the number for last year.

The struggle for the city's heart and soul seems to be accelerating even as polls show that the majority of Israelis - if not Jewish Jerusalemites - say that they would make concessions on the city as part of a lasting and final peace. Palestinian suburbs have been separated from the inner city by Israel's separation wall, while the new light railway, which when completed will connect West Jerusalem to Pisgat Ze'ev, will also separate Palestinian neighbours, further fragmenting the city's Arab population.

The key battle, however, is the one being fought in East Jerusalem over the corrosive issue of who is entitled to reside inside the city and to hold the blue ID card that brings with it entitlement to healthcare and social services.

The growing proliferation of 'facts on the ground' in East Jerusalem, combined with a lack of opportunity for Palestinians to build, has depressed Ziad al-Hammouri of the Jerusalem Centre for Social and Economic Rights. Hammouri says that fewer than 5 per cent of permits to build in East Jerusalem are processed, and that when they are they are often too expensive for Palestinians to be able to afford them. The result is an inevitable pressure not to remain.

'You know I feel Jerusalem is a hopeless case. I really feel that it is finished,' he says. 'The Israelis seem to have a plan to connect the west side of the city through the east to the west of the Old City via building and settlement. It will push Palestinians to leave the city.'

The perception of a siege mentality in many Palestinian neighbourhoods is understood by some Israeli analysts, among them Professor Shlomo Hasson, who is a lecturer in geography at the Hebrew University and a former town planner. 'The building of the separation wall has split the east of the city from the West Bank,' Hasson said. 'It blocks the exit opportunity for the Palestinian population and makes them feel besieged. The result is a blockade of Palestinians in the city.

'They are not concerned so much about nationalism,' he suggests. 'They are concerned now about survival.'

In the Arab quarter of the Old City those words are borne out in street after street. Many families who kept tiny homes in the Old City also had larger houses beyond what is now the separation wall. But fear of losing their Jerusalem IDs has led to an influx of people into these lanes to preserve their status as Jerusalemites, resulting in terrible overcrowding.

To preserve that status requires the production of multiple proofs that the resident's 'centre of life' is in Jerusalem, not elsewhere. In a small courtyard behind a metal door just off the Via Dolorosa lives the extended family of Abu Azim, an electrician, and his brothers - 40 people in all - occupying a series of tiny apartments.

'It is too expensive to live elsewhere,' Azim says. 'And if we find somewhere else our IDs are at risk. So people stick to their small shops to keep their residency status.'

As we talk an unseen woman shouts down: 'Don't mention me! I'll get in trouble with the ministry.'

A neighbour - who asks to be identified only as Umm Ibrahim - describes what kind of trouble. 'My daughter got married three years ago. She has a child and lives in a room next door,' he said. 'When she went to apply for her child allowance they came to make a site visit to prove that she was here. She was out - at the market or the kindergarten. Now they say she does not reside here and is not entitled to her allowance.'

Hasson believes that one outcome is that those on the 'Israeli side' of the wall may undergo the same process of assimilation as Israeli Arabs did. But Israel Kimhi, head of research at the Jerusalem Institute for Israel Studies, and a former town planner, is not optimistic that a solution to the problem of Jerusalem can easily be found.

'It's best to talk to God on that one,' he said, only just managing to laugh. 'There is no question about it. The wall has caused a lot of problems for East Jerusalem. It is harming the economy of the entire city. These acts of violence by those from East Jerusalem this year, it comes from individuals, not groups. But it is a bad indicator.'

Earlier this month the Israeli Prime Minister, Ehud Olmert, claimed that the Israeli-Palestinian peace process was edging ever closer to a successful outcome. Many Palestinians raised their eyebrows at that suggestion. But on all sides it is acknowledged that the future of Jerusalem remains intractable.

In the battle to come, one new force may be coming to the fore. The ultra-Orthodox - once a minority in the city - have swelled in numbers and political power, now controlling the municipality. More than 56 per cent of Israelis generally are ready to give up control of Arab neighbourhoods in Jerusalem in exchange for peace. But 76 per cent of the ultra-Orthodox are against it.

And if the majority of the ultra-Orthodox are committed to keeping hold of the Holy Basin - Jerusalem's heart and home to the major shrines of three religions, Judaism, Islam and Christianity - for others it is simply a question of nationalist sentiment.

'Just look at the facts,' said Barbara Noble heatedly in Ben Yehuda Street. 'I don't think that there is anything left for us to give back. We give back terrorists [to Hizbollah in Lebanon] including one who clubbed a child to death. And they give us back dead soldiers.

'There is always this insistence that we can make things right in the end by giving something up. But when was the last time Britain or the US gave up some of their territory?'