Pacing a small meeting room buried deep within the labyrinthine upper floors of the Foreign Office, the new British ambassador to Israel looks harried.

"Not enough electric sockets here," he says with an amiable grimace, before sitting down and launching into a high-speed shopping list of new bilateral initiatives and programmes that make up UK-Israel Science Day - one of the reasons for his trip to London this week.

So far, so bureaucratic. But David Quarrey's record shows he is no box-ticking - or easily boxed - diplomat. One of the FCO's most senior advisers on the Middle East, he was a private secretary to Tony Blair while he was prime minister and headed the UK's mission to the United Nations Security Council.

And then there is the arguably more mundane fact that nevertheless made the headlines: he is Britain's first openly gay ambassador to Israel.

What is it like being a prominent, openly gay figure in the Holy Land? A pause. For a moment, the dispassionate diplomat vanishes and a smile flickers. "It is not an issue because Israel is such an open and diverse society. And Tel Aviv is such a gay-friendly city."

Israelis might disagree with what you say but it is a democratic culture

Mr Quarrey was in Israel when an Orthodox man went on a stabbing spree at Jerusalem Gay Pride, leaving one teenage girl, Shira Banki, dead. The ambassador was clearly moved by Israel's reaction to the attack. "I went to Jerusalem Open House [an LGBTQ community centre] and met their youth group. I was impressed that the prime minister, the president, numerous cabinet ministers - from a real cross section of Israeli political culture - all came out very strongly and in sympathy for the community there. Even in that difficult situation there was plenty of support there."

For Mr Quarrey, such pluralism is embedded in Israeli culture, and for this he shows deep appreciation. "I relish the fact that you can have an argument about any kind of issue in Israel and people will listen to you. They might disagree with what you say, but it is a culture that is democratic in the more-than-political sense."

He also feels personally embraced by Israeli society. He and his partner have settled into life "incredibly quickly. I have visited Israel many times before, so part of the pleasure of being there is that I have had an opportunity to really get to know the country. We are both enjoying it, we've had an incredibly warm reception."

As a diplomat, Mr Quarrey sits comfortably within the auspicious British foreign service tradition of cool-headedness and studied impartiality.

Riling at the suggestion that the FCO, once labelled the "Camel Corps", harbours any pro-Arab bias, he says: "I would not accept that characterisation of the FCO. It's outdated. I don't think people have a simplistic or overly critical view of Israel."

He stresses that in the wake of the Paris attacks it is "inevitable and desirable" that the UK keeps increasing its security co-operation with Israel, especially because "Israel does face many of the same challenges that the UK does".

However, he indicated that closer military and intelligence ties will not prevent the UK from making clear its frustration with Israel over the peace process.

"There is a lot of concern about lack of progress in that area. It clearly is a difficult situation but that does not mean that people don't want to see Israel trying to move things forward, trying to make things better where it can.

"There are more things that could ease the situation, for example, taking more steps to ease the situation in Gaza along the lines of what Israel has been doing recently, or improving economic conditions in the West Bank."

Mr Quarrey dismisses the point often made by the Israeli government that the EU's guidelines on labelling products from the settlements would encourage BDS activists across Europe.

"We supported the EU move. We don't think there is any connection between those guidelines and boycotts. Since our own guidelines were introduced, the volume of Israeli exports to the UK has doubled. This is not a boycott. It is about giving consumers the info they deserve to have."

He does concede, however, that the extent and importance of economic ties between the UK and Israel may have been underplayed, and needed more promotion.

"There are big concrete, tangible benefits that result from those ties… and the coverage of BDS sometimes has the effect of drowning out other more positive stories," he says, with meticulous balance.

In many ways, Mr Quarrey is a very British man. He is also something of a traditionalist. He explains that one of the reasons he particularly likes living in Tel Aviv's Ramat Gan - the location of the UK's ambassadorial residence for many years - is that "the Brits have been there since the 1950s. I like the fact that a lot of people who live nearby remember it as such."

As a restrained Englishman, how will he cope with the pushy, emotional Israelis? "I really enjoy working with Israelis. I like the intensity." And as he says himself, Israel is an open society with "fantastic intellectual traditions". Perfect for the thinking man's envoy.