I respect free choice, but covering the face is not compatible for people to engage in society, and should be banned - Denmark, Bayern, and Austria are addressing problems of ostracising themselves from others, especially for identification or in classrooms.
Many muslims oppose the burqa against a Saudi-brand conservative model, e.g. in Morocco their sale is illegal, where terrorists used burqas to hide bombs and weapons, many religious scholars in Egypt. And although I disagree to violence and Islamophobia, in the current climate is a security risk for the women themselves.
And indeed on the topic of free choice, a person's freedom ends where others' freedom to safety (due to earlier highlighted concerns), and being able to talk to someone face to face ends, is endangered. And often there is no free choice involved in this decision, as they would face very bad consequences if they decided to remove them (only for some, yet defend the burqa in fear of repercussions).
Britain wants to be accepted but this is against proper social engagement, identification by police and authorities, and against their welfare, which seems to me, valid reason to ban the burqa in this country