There are several issues, not all of which are easy to separate and delineate clearly. Here are some (ignoring the security aspect):
1. Dress code - what it is acceptable to wear in certain social situations. You don't need laws for this, but you can have local rules. E.g. a bank or court of law could insist that people do not enter its premises in disguise; schools could insist that teachers do not wear masks (or, for that matter, bikinis). "Public decency" is such a local rule, because there is no specific law that I am aware of which bans nudity in public.
2. What dress cannot be accepted in public. These would include paramilitary uniforms or similar which flout the principle of the rule of law whereby law is set by Parliament and administered through constitutionally appointed bodies. This requires no specific legislation as the ban on the uniform is implicit in the ban on the organisations they symbolise. It would include other banned organisations who identify themselves by "uniform". (This requires a degree of common sense: you wouldn't want to arrest somebody who's going to a party as a Klansman - no, you wouldn't, would you?).
3. Women's rights. This is where the burka usually comes in: is this a symbol of the oppression of women, or a free expression of a woman's right to dress as she pleases in the light of her own religious conscience? Well, I for one am sure it's both, but would maintain that while it is invariably true of the first proposition ,it is only rarely so of the second.
None of which has answered AOG's question. So I'll come to that now. Enforce point 1: the burka has no place in the court room or the school. On point 2 it could be argued (and has been on this forum, if not this thread) that the burka IS a uniform, and what it symbolises is an extreme Islamism that despises its host community and refuses to make any adjustments to it. This is an analysis I subscribe to, but I oppose the ban, not because I don't know (and hate) the fascist doctrine the burka represents, but because the Islamist threat should be attacked directly and by other means, not through attacks on peripheral symptoms. I don't really like banning things, either, having a broader concept of freedom of expression than many of the "AB Friends of ..." faction whom I know and love. Point 3 is interesting for more than one reason. What Private Eye used to call the "wimmin's" movement is strangely silent on the issue, is it not? Remember that early campaigners for women's rights attacked the bustle and the corset for being (at least culturally) coercive. I think there was even a H&S angle employed. Burka = rickets would be the modern take. It is argued that the ban would be liberating for the "oppressed" majority. One post on this thread suggested the opposite. Who can adjudicate that? What I do feel reasonably certain of is that the vast majority of Muslim women who don't wear the burka, but live in areas where many do, (with the implication that the full veil is the minimum requirement of "modesty", and that those wearing anything less have become somewhat Westernised) might welcome a ban.
Anyway, it's a no from me, AOG. But I still hate it as much as what it represents hates us.