The United Kingdom Independence Party wants a full ban on veils covering the face.
The burka and other face-covering veils worn by Muslim women should be banned, the UK Independence Party says.
Ex-UKIP leader Nigel Farage, who leads UKIP's 13 MEPs in Brussels, told the BBC's Politics Show they were a symbol of an "increasingly divided Britain".
He also said they "oppressed" women and were a potential security threat.
But Schools Secretary Ed Balls said it was "not British" to tell people what to wear in the street, and accused UKIP of indulging in "unpleasant politics".
Some European countries, including France, are debating banning the burka, but the issue has sparked controversy when it has been raised in the UK.
UKIP is the first British party to call for a total ban, after the BNP called for it to be banned in Britain's schools.
But Mr Farage said: "I can't go into a bank with a motorcycle helmet on. I can't wear a balaclava going round the District and Circle line.
"What we are saying is, this is a symbol. It's a symbol of something that is used to oppress women. It is a symbol of an increasingly divided Britain.
"And the real worry - and it isn't just about what people wear - the real worry is that we are heading towards a situation where many of our cities are ghettoised and there is even talk about Sharia law becoming part of British culture."
A "different" culture was "being forced on parts of Britain and nobody wants that", added Mr Farage, but he denied the policy was an attempt to grab votes from the BNP, insisting it had "nothing to do with the BNP".
"There is nothing extreme or radical or ridiculous about this, but we can't go on living in a divided society," he told The Politics Show.
He said his party was seeking to ban "covering of the face in public places and public buildings" but said it had not yet worked out such a ban would be enforced.
Mr Balls said he was not surprised by Mr Farage's latest policy announcement, but he said no "sensible" or "mainstream" party in Britain would back a ban on face veils.
'Freedom of speech'
He told The Politics Show: "I wouldn't want to be part of a religion myself where we said to women and girls you have to wear a veil, but I also would not want to be in the kind of society where people were told how to dress when they walked down the streets.
"So the idea that we would tell people that you cannot wear a veil in public, I think that's not British, it's unfair, it's not consistent with our traditions of liberty and freedom."
Salma Yaqoob, leader of the anti-war Respect party, also criticised UKIP's proposed ban on the burka.
"I certainly wouldn't want to wear it myself, but then to take it to a step where they are going to ban it because I feel uncomfortable with it is something I would say is very un-British because the British way of life is 'live and let live', freedom of speech, freedom of worship," she said.
"As long as they are not imposing it on anybody else they should have the right to wear it."
UKIP came second in last year's European elections, ahead of the Labour Party, but Mr Farage quit as leader to concentrate on trying to become the party's first MP at Westminster.
His successor, Lord Pearson, has said he wants to step up the party's campaign against radical Islam.
He told the Times the party was taking legal advice on how the burka, or any veil covering a woman's face, could be banned in public places and in private buildings such as airports.
French President Nicolas Sarkozy has said the full burka is "not welcome" in France, but did not explicitly call for a ban, saying "no one should feel stigmatised" by any eventual law.
A French parliamentary report on the issue is due out at the end of January.