Almost 500 children were abducted from the UK and taken abroad illegally last year, according to figures released to the Guardian under the Freedom of Information Act.

There were 336 cases of child abduction reported to authorities in the UK in 2008, an increase of 20% on 2005 figures. These cases involved an estimated 470 children last year. More children were taken illegally to Pakistan than any other country (30 cases in 2008), followed by the USA (23), Ireland (22) and Spain (21). Other abduction hotspots included Australia, France and Egypt.

Abductions usually occur when marriages break down between couples of different nationalities, and the parent who is not awarded custody kidnaps their children. Now is peak abduction season, as children are taken abroad during the school summer holidays and not returned.

Usually, the cases aren't publicised as they are dealt with in the family courts where reporting restrictions apply to any cases involving the welfare of minors. But they are becoming increasingly common – when the Guardian spent a day in a family court in London recently, eight out of 14 cases heard involved child abduction.

The government has little power to intervene in around 40% of all abduction cases, as they involve children being taken to countries not signed up to the Hague convention, an international treaty which obliges nations to promptly return children wrongfully retained in their jurisdiction. Experts say it is often almost impossible for mothers to get back children taken by their fathers to Islamic countries with sharia law, such as Saudi Arabia, which prioritise male parental rights.

But recently Gordon Brown and the new health secretary, Andy Burnham, have personally intervened in the case of Nadia Fawzi, then a four-year-old British girl taken from Wigan to Libya by her Libyan father.

A month ago, Burnham, the girl's MP, flew to Tripoli for meetings with the Libyan justice ministry and police force about the case, and Gordon Brown asked the Libyan leader, Colonel Gaddafi, to help return the girl to the UK when the two met for the first time at the G8 summit in Italy.

Nadia was picked up from her home in Wigan by her father, who said they were going to a party. But instead, he drove to Manchester airport, where he was captured on CCTV buying plane tickets to Libya. Nadia hasn't been home since.

Her British mother, Sarah Taylor, saw her daughter on a few occasions in the months after her abduction, but has had no contact with her since Christmas 2007.

Taylor has spent the last two years doing everything in her power to be reunited with her now six-year-old daughter. Libya is a notoriously difficult country to negotiate with on such matters – it has not signed up to the Hague convention, and so the UK government is limited in the support it can offer.

In November 2007, Taylor took a drastic step. She sold her house, gave up her job and moved to Libya to fight through the local courts for the custody she had already been awarded in the UK courts after her marriage to Nadia's father broke down.

After a long and difficult battle in the labyrinthine sharia legal system, Taylor won full custody of Nadia in 2008. But her ex-husband refused to comply with the court order, and despite quiet but firm interventions from the Foreign Office and assorted other agencies in the UK and Tripoli, he still has the little girl in his care. Or at least Taylor believes he does – no one is entirely sure where in the Libyan capital father and daughter are currently living.

Burnham told the Guardian he is hopeful that mother and daughter will soon be reunited.

He said: "This awful injustice and crime has now been raised at the highest level and we now expect swift action. This is a story about a young girl taken illegally off the streets of my constituency and I will go to any lengths to right that wrong."

In 2008, 134 out of the 336 cases of child abduction involved children taken to non-Hague countries, including Bangladesh, Russia, Iraq and Nigeria. These cases are dealt with by the Foreign Office, while Hague cases go through the Ministry of Justice in England and Wales, and the Scottish and Northern Irish court services.

Scotland dealt with nine cases last year involving 12 children. In Northern Ireland last year there were 12 reported instances, involving 20 children taken to the Republic of Ireland, the USA, Israel, Germany, Finland, Poland and France.

The increase in cases is an "inevitable consequence of greater migration", according to Andy Elvin, chief executive of the charity International Social Services, which helps parents secure the return of their children. "Child abduction is a growing trend as we have an increasing number of families where at least one parent is originally from overseas," he said.

Denise Carter, director of Reunite, a UK charity specialising in international parental child abduction, said: "The increase in international travel and more and more people travelling on short-term contracts and changing their habitual residence also has an effect."

Figures from Reunite show that since 1995, the number of children abducted from Britain and taken to another country has risen by 93%.

The government's figures clearly show the effect of EU enlargement. For example, until Latvia joined the EU in 2004, there had been no reported cases of children being abducted there from the UK in the previous four years. But in 2005, three cases were reported, and there has been at least one new instance every year since.

Similarly, while there were no reported abductions to Poland in 2003, the year before the country's EU entry, there were 10 in 2006 and 2008. "We expect to see more and more cases from countries like Poland as the years go on and more couples marry, have children and get divorced," said Elvin.

A Foreign Office spokesperson said: "When there is no international mechanism in place, usually the left-behind parent's only option [other than trying to come to an agreement with the other parent] is to file a case in the courts of the country where their child has been taken. However, pursuing such a case will often be expensive and there is no guarantee the courts will decide that the child should be returned to the UK."