Senior police officers are urging David Cameron to resist pressure from Tory MPs to opt out of European police co-operation after teacher Jeremy Forrest was apprehended under an EU arrest warrant on suspicion of abducting teenager Megan Stammers.

The Observer has learned that senior British officers working at Europol's HQ in The Hague, as well as UK-based officers, are lobbying the UK government on the benefits of EU cross-border crime fighting and investigations, ahead of a crucial decision on the UK's participation in police co-operation to be taken in 2014. The issue has come into sharper focus after Forrest was apprehended under an EU warrant on Friday following successful co-operation between EU forces.

More than 100 Tory MPs recently went public to demand that Cameron uses his right to opt out of EU crime and policing, including the arrest warrant, in order to prevent further loss of sovereignty to Brussels.

The issue is dividing the coalition parties, with the pro-EU Liberal Democrats determined to fight any plan to dilute the UK's role in what is widely regarded as one of the more successful areas of EU cross-border co-operation. Policing at EU level, including use of the warrant, has been used to track down and bring to justice paedophiles, international drug dealers and terrorists over recent years.

A source close to Nick Clegg said: "It is utterly extraordinary that some people seem determined to put anti-European ideology above tackling crime. This week has demonstrated what a crucial tool the European Arrest Warrant (EAW) is for our police. It's time we listened to them rather than people who refuse to accept anything good can come out of European co-operation."

Jeremy Browne, the Liberal Democrat Home Office minister, said: "The EAW is a powerful tool for the police in bringing people to justice and the case of Megan Stammers is another example of its benefits."

The arrest on Friday of Forrest, who fled abroad with Megan more than a week ago, was the result of close co-operation between UK and French forces. EU arrest warrants, introduced in 2004, have been used with increasing regularity in a variety of cases and allow for quick extradition of suspects to their home countries.

Commander Allan Gibson, director of professional standards at the Metropolitan police and spokesman for the Association of Chief Police Officers on extradition and mutual legal assistance, told the Observer: "There can be little doubt that the European Arrest Warrant is much quicker, simpler and cheaper and the exercise of justice is more efficient and effective with forces in several countries co-operating.

"Previously, extradition from countries like Poland, Germany and France could be very slow and bureaucratic. The EAW is the most effective of the instruments that would be potentially affected by the 2014 decision."

Forrest – Megan's maths teacher at Bishop Bell C of E school in Eastbourne – will not fight extradition proceedings and has agreed to return to the UK as soon as possible, his lawyers said. It is understood it will be a number of days before he is returned to the UK as he waits to appear in court in France on Tuesday. Megan's parents have already been in contact with their daughter by phone but have remained in the UK as they await her return, a Sussex police spokesman said.

Officers said they planned to speak with Megan once she had met with mother Danielle Wilson and stepfather Martin Stammers, he said. Megan was reported missing when she failed to turn up for school last Friday, and it emerged that she had travelled with Forrest to France the previous evening, sparking a highly publicised search.

In a public letter earlier this year, more than 100 Tory MPs urged the government to pull out of EU police co-operation, including the EAW. "We do not wish to subordinate UK authorities to a pan-European public prosecutor. We do not want to see British police forces subjected to mandatory demands by European police under the European Investigation Order. We have deep concerns about the operation of the European Arrest Warrant for our citizens. We want the UK supreme court to have the last word on UK crime and policing, not the European court of justice," they said.

They said they wanted the UK to withdraw from 130 measures under the EU crime and policing plan by 2014 – but to retain the right to opt back in to any specific policies deemed vital on a case by case basis.