I first met Mark Sofer in a humid Mumbai car-park in November 2008. The multiple terror attacks on the city - which included an assault on a Chabad centre - were still in progress, Israeli security teams were scouring mortuaries to discover how many of the country's nationals had been killed, and the Israeli ambassador had agreed to give an impromptu briefing to reporters outside the consulate. I remember marvelling at Sofer's unruffled performance in that hectic situation, and despite his impeccable Hebrew not containing a trace of an accent, I was not surprised to learn later that he was born and bred in London.

The 57-year-old Sofer has since left the diplomatic service for one of the most difficult jobs in Israel. As the new president of the Jerusalem Foundation, he is in charge of an organisation dedicated to fostering co-existence in a divided city. His role, at a time of economic uncertainty, is to run the global fund-raising operation which helps pay for the communal and cultural projects with which the foundation aims to improve the lives of all Jerusalem's citizens.

But that is not even his main challenge. He is only the second president in the foundation's 45-year history, filling the shoes of founder Ruth Cheshin. She managed to keep the organisation above the city's tempestuous politics and toxic inter-communal relations, and Sofer must do the same. That is probably why the foundation's board selected a veteran diplomat for the job. And old diplomatic habits die hard, it seems - over half the questions in our hour-long interview Sofer answers with a polite smile and even politer evasion.

Even when asked to pick a favourite project from over 2,000 which the Jerusalem Foundation has funded across the city, he demurs. "That's not a simple question," he excuses himself. "If you look at what we have done for over 40 years in every field -in every community centre in the city, in East Jerusalem, the building of the Inter-Cultural Centre, the Mishkenot Shaananim convention centre, the Teddy Stadium [named after foundation co-founder, Jerusalem's legendary mayor Teddy Kollek], and parks, scholarships for hundreds of young people, the college for Haredi women - choosing one outstanding project is really comparing chalk to cheese.

He also points out that a lot of the foundation's work goes on "beneath the surface, without publicity". Indeed, most Jerusalemites are not even aware that it has distributed £900 million to projects in the city, more than any other philanthropic organisation. Its tulip symbol, shaped as a turret from the Old City wall, appears on signposts and plaques throughout Jerusalem, but manages to be both ubiquitous and unobtrusive, simply part of the scenery. But the city as it is today would be unimaginable without the foundation.

We believe we have to supply everyone in the city with culture

And having such power means that it has often been a target for local and national politicians, eager to influence its policies. Sofer will not be drawn on this, saying only that "it is very difficult to connect between all the conflicting poles and the needs of the city". But it is no secret that at least two previous mayors, Ehud Olmert and Uri Lupolianski, both fought behind the scenes to control the foundation, only to be repulsed. Olmert even tried to set up a rival organisation to attract donors away but the initiative ultimately folded.

Relations with Jerusalem's current mayor, Nir Barkat, are more relaxed and just before our interview, Sofer attended the dedication of a new, all-weather football ground in the Arab Beit Zafafa neighbourhood along with Barkat.

Sofer, who emigrated to Israel on his own at the age of 18, has a long history of dealing with politicians. In the 1990s he served as diplomatic adviser to then foreign minister Shimon Peres, and afterwards, as head of the Middle East economy unit at the ministry, he was closely involved in dealings with Israel's Arab neighbours at a time when the optimism inspired by the 1993 Oslo peace accords still ruled.

Some of his foreign ministry colleagues from that period have recently spoken out against the direction of Israel's diplomatic corps under the leadership of the current foreign minister, Avigdor Lieberman, which, they say, is ruining Israel's relations with the outside world. While Sofer's body-language certainly does not broadcast satisfaction with the situation, on the record he is more cautious.

"In order to continue operating a serious foreign service, we need to refrain from expressing our political views," he says of retired ambassadors. "Otherwise, it will be the end of the service. It is a much more complicated period now than the 1990s. I certainly don't want to pass judgement on foreign ministers.

Sofer, who received his first degree in economics and international relations from the London School of Economics and a Master's degree in political science from the Hebrew University, held his most senior diplomatic positions during the post-Oslo decade. He describes his three years as ambassador to Ireland as "very uneasy". Those were the years in which the Second Intifada broke out, and "the Irish people had an unfriendly attitude towards Israel, and since, at the time, their economy was booming, they had the self-confidence to actively pursue foreign policies as a wealthy European nation."

Despite the difficult period in Dublin, Sofer, ever the diplomat, stops short of describing Ireland as "hostile" to Israel, but he certainly feels much happier talking about his last posting, as ambassador to India.

"We have a fantastic and dynamic relationship with India, and it's only getting better. Not just with the government but also on a people-to-people level."

And maybe his four years representing Israel in the most diverse and seemingly most dysfunctional democracy in the world was the best preparation for his new job after diplomacy.

"It is hard to compare," he says, "but like India, Jerusalem has many demographic problems, and connections between the different groups are complicated. We believe we have to supply everyone with culture, wherever they live, but also in places where all parts of Jerusalem come together, and you can see that, for example, in the Science Museum, where you see Jewish secular and Haredi and Arab children all visiting."

While the foundation funds museums, Sofer's biggest worry is that the city itself "will be transformed into a museum, where people just come and look at the exhibits. Not a place where people actually live. The trend of certain groups and young people leaving the city is leading to that. Hopefully we can reverse that trend and keep Jerusalem a living city."