David Lidington is a very moderate man. His voice, while slightly too staccato to be restful, has the assured, controlled tone of a natural diplomat. He needs it.

As Europe Minister, he represents the coalition government on an issue that has sparked vicious infighting in the Conservative camp on several occasions. Since he took over the job at the May election, his work has made remarkably few headlines – probably an achievement in itself.

It is this measured approach, as well as his moderate stance on the EU, that propelled him to his current position. Combative Euro-sceptic, Mark Francois, held the Europe job in opposition, but the anger that endeared him to Tory members made him a liability in the sensitive environment of coalition politics.

To listen to Lidington, Brussels’ notoriously tortuous negotiations are little more than a chat in Starbucks. "The closest to ‘smoke-filled rooms’ I get is informal meetings over dinner or a cup of tea with other Europe Ministers", he says. "And often these are the most productive meetings."

Parachuted in after the election, he seems to be settling in well. When we meet, he waxes lyrical about the Foreign Office’s grandiose architecture and unintentionally humorous Imperial-era artwork. But despite the mild-mannered appearance, Lidington can be blunt. Visiting the University in an attempt to boost the meagre numbers of British graduates applying for jobs at EU institutions, he says that the reason for the shortfall is simple: "The EU has an image problem right across the UK, not just with students."

"It is our responsibility in Government to explain the facts about our membership and the benefits that it brings as well as where we want to see change. We’re committed to remaining an active member of the European Union and that’s why the lack of interest amongst UK graduates in an EU career is worrying."

He adds: "Yes, it’s true that there are sometimes silly media stories that distort something that’s going on in Europe in order to get a headline. It’s also the case that sometimes the EU does silly things. You do get some regulations that meddle too much in the detail of life, that interfere with things that frankly ought to be left to member states to sort out. I think also that there is a problem, which is not confined to the United Kingdom, about a loss of confidence in EU institutions."

There is a sense that the scheme he is promoting may be a tough sell. Lidington claims: "Anecdotal evidence suggests that graduates either don’t know enough about the opportunities, are put off by rumours of difficulties getting in or the perception that the work is dull and bureaucratic." However, the fact remains that the so-called concours system that EU institutions use to recruit graduates is a daunting process. Albeit one recently made, slightly less onerous policy – the duration has been cut to only nine months. UK graduates are also expected to be proficient in either French or German.

Lidington adds that internships are a major advantage in EU recruitment, but admits that his department is unable to fund any schemes to help those from poorer backgrounds who might be unable to afford to take time out as interns.

"It’s no secret that the government is strapped for cash at the minute," he says. "Every department is looking for economies. We have found the money to maintain the Europe Fast Stream programme, which provides opportunities for a limited number of British graduates each year to get into the British civil service and then to be groomed to go into European institutions. That has meant finding money at a time when there are a lot of other demands on a finite public purse, so I don’t want to pretend that there are huge hidden funds somewhere in Whitehall, because there are not.

"What I do think is clear is that in large part the problem that we have is simply a lack of awareness by students and those advising them, that these career opportunities exist and that these are very challenging, interesting and well-rewarding jobs. That’s something that we are trying to promote and we have very strong support from senior members of the British government and also from European institutions."

Asked whether publicity is the Foreign Office’s only tactic to recruit more British graduates for European service, Lidington replies: "Yes, for the moment."

On slightly more politically sensitive topics, Lidington’s composure remains largely intact, although he seems slightly more flustered than usual on the contentious topic of the Conservatives’ European allies. In pulling out of the centre-right EPP grouping to found the tougher-talking ECR last summer, David Cameron fulfilled a long-standing pledge to the Tory rank-and-file. Yet at the cost of a series of rows over the party’s controversial new Eastern European allies, some of whom have been labelled anti-Semitic by opponents. The ECR also has far less political clout than the EPP, boasting only 54 MEPs against the 265 still residing in the Conservatives’ former home.

I ask Lidington whether his work representing British interests in Brussels has been helped or hindered by his party standing outside the mainstream in this way.

He hesitates for a moment, then replies: "No, for two reasons. First that the ECR is functioning very effectively as a cohesive group in the European parliament. [EU Commission] President [José Manuel] Barroso would not have been re-elected as commission president had he not had the support of the ECR as well as the EPP, and a good working relationship has been established in the European parliament between those two centre-right groups.

"Certainly, in the meetings which I and the foreign secretary and the prime minister have had with our centre-right counterparts around Europe, what we find is an acceptance of the decision which the conservative party took. It’s water under the bridge and we look for ways in which to have a very good, constructive set of relationships...without reopening that particular question."

Asked whether this "good working relationship" means that the two groups are becoming ever closer, Lidington’s response is rather odd. He denies that a merger is on the cards, despite the issue never having been raised in our conversation.

"No, I would suggest that they’re – I don’t want to suggest that they’re going to merge because that’s not going to happen. What is happening is that the groups are finding ways of working and cooperating together. The phrase David Cameron uses is that we would rather be good neighbours than unhappy tenants. That’s how he sees the relationship."

This last pre-emptive denial gives a glimpse of the danger lurking under the surface for David Lidington. One clumsy sentence, an unwelcome turn of events abroad or even just a slow news week – any of these could thrust him into the spotlight and even split the coalition. You can be sure that the mild-mannered man’s work is under intense scrutiny.