Only 5% of British Muslims choose to wear the veil.
All the women that I know that choose to wear it are under 35 - the mothers, aunts and grandmothers don't and never have done. Very often their sisters don't.
The explanantion is the Q'ran states that women should dress modestly and be covered. Different people interpret that to mean different things. Some Muslim women believe it means that their body parts that define them as women should be covered, whilst those that wear the veil interpret it as meaning the whole body should be covered.
As I understand it there is no requirement to wear the veil where men are not present - the infant classroom, for example.
The women of my acquaintance that wear it seem to be making some sort of political statement - at the very least they are politically motivated and somewhat radical.
Of course, I do not know all the women that wear it and their reasons may be different.