Alice Thomson is against the wearing of the burka. She's not in favour of banning it, only of making it clear that we regard it as 'socially unacceptable'. I think that's the right approach for anyone who does so regard it, leaving people free both to wear what they want and to express their views on the subject.
But Thomson uses a dubious argument in making her case. She says that facial expressions are 'crucial for human interaction'. I suppose she could simply mean by 'crucial' very important - and if so she would be right. But even important things are sometimes bypassed, put aside for other, equally or more important, reasons. Her use of 'crucial' in this context suggests something stronger than important, something like indispensable. And facial expressions, though they are normally much used in interpersonal communication, are not indispensable to it. People can communicate with their backs turned, or from one room to another, and on the telephone and in writing. Or, to give an example Thomson herself alludes to, the blind communicate with others without being able to see their faces. Communication may be more difficult where we don't have access to facial expressions, and misunderstandings more common. And this may suffice as one among other reasons for opposing public covering of the face. But one doesn't need to overstate the argument. Doing so in fact weakens it. (See also this post.)