The Burka (face covering) and Hijab (head covering) are personal choices, they should not be forced upon any woman and if they are that person who is forcing them is not following Islam properly. When that's taken into consideration its the same as other personal choices, theirs to make.
Like others already said, when required for things such a license's and so on they will always remove them, you cannot obtain a photo I.D without a photo after all.
Many of the points raised in criticism of the burka are often wildly hypocritical or factually incorrect. For instance Sikhs are allowed to carry knives in the UK due to it being one of their religious tenants where as everyone else is not. Many schools with no jewellery policies allow the Christian Cross to be worn on a chain and so on.
I am a Muslim, i have 2 sisters, 1 who has never worn a Hijab or Burkah, one who chooses to. My dad often asks her to not wear it for fear of her being targeted (again). But its her choice and she wants to wear it and so she does.
We live in an age of fear, and so its understandable to fear what you don't understand, but please make the effort to get to know a group of people before you judge them, i guarantee things aren't as black and white as the media makes them out to be.