It's a moral minefield.
On the one hand there is the issue of freedom. Should people be allowed to wear anything they like? Surely in a liberal society that's the ideal. People can wear what they want when they want. Except they can't. A nudist would be arrested if he walked into the Arndale in his birthday suit for example. And why? Because it's culturally unacceptable. Would he actually be causing any harm?
Then there is the security thing. I've worked in places where you aren't allowed in with a motorcycle helmet on because nobody can see your face. Yet burka clad women could walk freely in. Is that not hypocritical. I doubt it would be legal for a shop to ban people wearing the burka from entering.
The debate around the burka itself is tricky too. Some argue it is a symbol of oppression. Others that it is liberating because women aren't judged on how attractive they are. How many of the women wearing it do so through choice? I have no idea. How many merely think they freely choose to wear it after a lifetime of conditioning and brainwashing?
A flat ban doesn't appeal to me. Bans in certain situations eg the shop example may be justifiable. If a shop has a policy of not allowing helmets they should be free to stop anyone wearing a burka from entering unless they reveal their face. If it is being done for genuine security reasons I don't think there's an issue with it.
As always anything to do with religion has one answer and that is education. Give anyone a childhood education free from religious bias, expectation and conditioning and they are highly unlikely to choose a religion. If they do and then choose to wear the burka then it's their choice and who is anyone to question that? We can't give immigrants that education but faith schools should not exist in the UK. No child should be branded a Christian, Jew, Muslim just because their parents are. You wouldn't call a 5-year-old a Tory, a Feminist, an Keynesian because of their parents views would you?