British political leaders should hold cross-party talks on immigration to avoid a dangerous "arms race" towards tougher policies, a Labour MP says.

Keith Vaz said it was vital to find consensus to avoid "fringe parties" filling a vacuum amid fears over the impact of new arrivals from Bulgaria and Romania next year.

Vaz, who is the chair of the Commons home affairs committee, also called on the British government to carry out in-depth research into the likely impact of the end of restrictions on arrivals from the newest EU member states.

"Rather as they did for the Royal Charter agreement after Leveson, Messrs Cameron, Clegg and Miliband should now sit down together and talk about this issue," he wrote in the Sunday Express.

"By doing this they will deny fringe parties the opportunity to fill the vacuum and demonstrate to the British people they want to engage purposefully and productively in addressing one the most challenging issues that our nation faces."

Prime Minister David Cameron heralded tougher curbs on unemployment benefits and NHS access for immigrants last week - issuing a warning people should not expect "something for nothing".

A failure to be sufficiently robust on the issue is blamed by some Conservative MPs for allowing the UK Independence Party to surge into third place.

Labour leader Ed Miliband had issued a "mea culpa for Labour's past mistakes" and Deputy Prime Minister Nick Clegg abandoned an amnesty policy for long-term illegal immigrants, Vaz noted.

"On this issue above all others we should listen to the British people," he said.

"They have been incredibly tolerant in the past, but they cannot stand abuse of the system.

"I do not believe they want politicians to play the race card. Instead, they want the immigration game to be played fairly.

"What is needed, however, is not an arms race on immigration policy among our party leaders, but a new consensus."

The MP questioned why the government had no estimates of expected arrivals from Romania and Bulgaria, saying the projections were "essential for government policy, from welfare benefits to the NHS".

"Research needs to be commissioned immediately, and we need to start a dialogue with the Romanian and Bulgarian governments," he wrote.

"We still do not know how many times (Home Secretary Theresa) May has visited Bucharest or Sofia to discuss the problem: she refuses to answers Parliamentary questions about it."

The recently-announced break-up of the UK Border Agency and its return to direct ministerial control at the Home Office was a good start but must not be simply "a re-branding exercise or a short-term fix to try to contain the campaigning zeal of UKIP", he said.

However the initial omens "are worrying", he said - pointing to a leaked memo from the head of the Home Office telling staff they will "still be doing the same job in the same place with the same colleagues for the same boss".

There should be a "ruthless change of personnel at the top", he said.

"The immigration debate is in the end about numbers. Vacuous statements about 'the best and the brightest' are meaningless. Every country wants to attract such people.

"Provided we get root and branch reform, ministerial focus, and a change of personnel at the top of the immigration service, then this week will have drawn a line in the sand."

-AAP