Has it been established in law that shopping centres have the right to refuse entry to "youths wearing hooded tops"

Yes. It is up to the management of ANY establishment to apply any rules they wish allowing entry unless it is on the grounds of religious, racial or sexual discrimination.

but not to burka-clad women?

They are not applying it to these because they believe it contravenes the above rules. As I pointed out, it does not.

And is there any indication that the managers of shopping centre want to refuse entry to burka-clad women? If so, why? If not, why not?

Please see this report and then ask why shop managers may or may not wish to ban the burka.

As to A woman may wear it to be consistent with her personal understanding of the requirements of her religion, or with her sense of modesty, or with the practice within her sub-culture, or I suppose for any number of other reasons.

The 'hoody' or hooded top is worn as part of a sub-culture and due to presure from peers. How is this different to the wearing of a burka?

Cheers

Dave.