Most people I know have absolutely no issue with Muslim women covering their hair. It is the full-face covering that is objected to as it is inhibitive to conversation as you can't see someone's facial expression.
Just as full-face covering is a cultural norm in some other countries, in the UK it is a cultural norm to remove any and all head coverings indoors.
This is possibly why there is such a culture clash.
The majority of white people I know would see it as downright rude and ill-mannered to wear ANY sort of head covering indoors, hat, scarf, baseball cap, anything.
I know nowadays, even lots of British people don't see it as such, but there will still be quite a few that DO.
I personally have many friends who wear a headscarf, but I find it too difficult to cultivate friendships with those women that wear a full-face covering, as it is too difficult to get 'into' a conversation with them as I cannot see their facial expressions. Over half of all communication is non-verbal, and wearing a full face covering has the effect of cutting out the majority of non-verbal communication.
If my friends that wear a headscarf admit that they find it difficult to maintain friendships with other Muslims that wear a full-face cover, how is someone NOT brought up in that culture meant to manage it?
I feel that it is perfectly possible for a woman to be a good Muslim, and follow the teachings of the Qu'ran while wearing a headscarf, while a full-face cover, in the UK, is unnecessarily divisive, and not religiously necessary.
A headscarf, yes, a full-face cover, no.