Tory grandee Lord Tebbit has warned of immigrants who try to "recreate their country" in the UK.
The former Conservative Party chairman said some were building "separate societies" and warned that immigrants from the "third world" had no intention of integrating.
Lord Tebbit also supported a ban on women wearing a full face veil in certain cases where it is essential to see people's faces.
He told Sky News' Murnaghan programme that his concerns about immigration were not over Bulgarian and Romanian people who could enter the UK after transitional controls expire at the end of the year.
"Let's not jump to that conclusion about immigration. The bigger problem that is caused in our cities is caused by immigrants from the third world who have got no intention of integrating here," he said.
"They are people who left their country, came here and are trying to recreate their country in our country.
"We don't have much of a problem with people like the Poles, the Czechs, the Slovaks or indeed French or Germans who come here, they're not the problem and I often have to remind people that in 1940 we were extremely glad to have a bunch of Polish immigrants come here, without them we would have lost the Battle of Britain and lost the war.
"Then when you look at the south-east of the European Union, there is a very grave problem because the borders are leaky and people come in through those countries here and our welfare system is much more attractive than theirs.
"So you've got to have some controls but don't think that the problem is all caused by Polish plumbers. It isn't."
Lord Tebbit, who in 1990 proposed his "cricket test", suggesting that immigrants should back the England team rather than that of their country of origin, added: "We are building not so much a multi-racial society or a multi-cultural society, we are building separate societies which really don't have much to do with each other."
On the issue of the veil he said: "So far as I'm concerned within the limits of common decency anybody should be able to wear whatever they like in the street or at home, but it comes to a different thing if the person who is hiding their face is for example your doctor or a nurse, you need to see their face in order to know what they are saying and what they are thinking.
"Equally, how do we know in a courtroom that the person who is giving evidence is the person that they say they are if we can't see their face. What's more, if they are lying, perhaps their face might give that away, particularly under cross-examination, so we have to say no to covering yourself up completely in that way.
"There is the additional problem that we have got a number of cases where men have disguised themselves by wearing traditional women's dress in pursuit of a crime so again there are dangers to it, but overall we must let people wear what they wish in general, but in particular situations where it is essential that we should see each other's faces, then the veil should be forbidden."
British people are bad at integrating into other societies and should realise that when "preaching about integration", according to shadow home affairs minister Chris Bryant.
Bryant said Brits who travel to resorts in Spain such as Torremolinos do not assimilate perfectly and therefore need to "get used to some facts".
Speaking at a fringe event at the Labour Party conference in Brighton, he said: "We British have to get used to some facts. We all preach about integration of migrants into society in the UK.
"Has anybody ever been to Torremolinos?
"I don't see Brits assimilating perfectly into Spanish society. I feel able to say this because I do speak Spanish and when we lived in Spain as a child I learnt Spanish, partly because the local kids threw stones at me because I didn't speak Spanish."