Senior detectives and politicians want to see the creation of a dedicated FBI-style task force to take responsibility for high-profile criminal investigations away from local police forces.
They believe a national police body would improve efficiency and produce quicker results.
But critics say such the changes would make no difference and the Home Office insists there are no plans for a review.
The debate comes as Cambridgeshire police request help from a specialist Scotland Yard murder unit in what has become one of Britain's largest investigations.
There are 320 officers hunting the two 10 year olds, who went missing from their homes in Soham, Cambridgeshire, 11 days ago.
Tony Arbour, a Conservative member of the Metropolitan Police Authority, is to table a proposal that the authority takes the lead in creating a national force for major crimes.
He told BBC News: "Every police force has enormous pride and they don't want to call in Scotland Yard.
"It's easy to see there could be rivalries, but if we bring criminals to book or perhaps rescue children, then I think we should put those squabbles aside."
Terrorism
He said the permanent expertise would prevent delays brought about by "ad hoc" major investigations by individual constabularies.
Britain currently has several national security agencies dealing with high-level crime such as terrorism, criminal gangs and organised crime.
They include MI5, the National Criminal Intelligence Service (NCIS) and the National Crime Squad (NCS).
But there is no equivalent for one-off criminal investigations such as murders.
In the US, the FBI has 11,000 special agents which take on terrorism, drugs, murders and child kidnappings.
This week, the FBI intervened to help secure the return of a four-year-old girl in California.
Bob Taylor, a former National Crime Squad detective, said: "My view is there should be a national police force where expertise can be mobilised in minutes or hours to move anywhere in the country where it's needed.
UK crime agencies
MI5: terrorism, espionage
NCIS: co-ordinates intelligence on major criminal gangs, eg football hooligans
NCS: drugs, organised crime
"When you put a burden like this on a small force that may not have had previous experience of handling large-scale inquiries, it can be problematic."
John Stalker, former deputy chief constable of Greater Manchester Police, told the London Evening Standard the present police system is "close to meltdown" and can place too much of a strain on small police forces.
But not everyone is so sure a centralised body is the answer and some fear it would bring an end to local accountability.
Lord Mackenzie, former president of the Police Superintendents Association, said: "I don't think a national crime squad or murder squad would add any value to this kind of inquiry."
And a Home Office spokesman said: "Setting up a single organised crime agency wouldn't be the answer."