There is an excellent libertarian and Conservative argument against a burka-ban as Dominic Lawson wrote in The Times

"it is absurd — morally and legally — to force women to be feminist against their wishes." and

"It would be analogous to the legislative fiasco of the banning of hunting with hounds, which occurred largely because Labour MPs regarded as deeply offensive the sight of the English gentry dressed in red charging around on horses "

The argument goes that it really is none of our business, nor the government's what people choose to wear but, in fact, as pointed out previously, it's not true that we don't have laws about what people can wear in public (for example the naked rambler) and at a legal demo I attended several people were instructed to remove half face masks by the police and their personal details taken.

It's also possible to make what looks superficially like a convincing feminist case for the burka

This argument goes -
'it protects the woman wearing it from the "objectifying male gaze", it is a response to a culture in which women are judged by appearance and expected to conform to normative standards of dress and grooming, it protects against harassment (well possibly not), it embodies a rejection of the cheapness and pornography of Western societies"……… and so on.

I agree with the observation that such a pseudo-feminist argument for veiling is apt to catch some 'professing liberals' unawares.

Yasmin Alibhai-Brown writes

"You people who support the "freedom" to wear the burka, do you think anorexics and drug addicts have the right to choose what they do?

This covering makes women invisible, invalidates their participatory rights and confirms them as evil temptresses.

Does it stop men from raping them? Does it mean they have more respect in the home and enclaves?
Like hell it does. I feel the same fury when I see Orthodox Jewish women in wigs, with their many children, living tightly proscribed lives.

Progressive Muslims come out daily against the burka, and against mothers who bind and swaddle their young girls in preparation for their eventual incarceration which they will accept without a cry – both un-Islamic customs.

Yes, the burka will be used by racists against us.

But while fighting racism we cannot allow ourselves to become apologists for another, abhorrent injustice"

I've discussed this issue with friends and hit the barrier of the 'harm principle' - that is to say that if the wearing of total body and face covering is a voluntary choice (even a political statement for some young single radical women) there's little a liberal state can or should do about it

However Alibhai-Brown's answer (and the French one) - would seem to be that in fact they are harming other people through their choice of dress by making it difficult for more socially restricted women to exercise any autonomy
In addition, Yasmin Alibhai-Brown quotes an incident in which one conspicuously veiled woman provokes a hostile response from other Asians, who are heard to mutter "Stupid women, giving us all a bad name. They should send them back."!

The wearing of the burka is NOT a religious requirement, it is uncomfortable and denies simple social activities like eating out etc
how on earth are you supposed to drive - although I understand Saudi women are not allowed to.

The 'security' argument has already been discussed although no one so far has mentioned the fact that the deprivation of sunlight is bad for health.

The real argument IMO is not one of secularism versus multiculturalism, it comes down to our understanding of what it means to be 'liberal'