Burkhas are a cultural choice, not a religious obligation (whether by the individual women or their menfolk - and some wearers I used to know were the women opting to wear it because of their culture) - but burkha wearers are a tiny tiny percentage of the Muslims in this country, so let's park that for now.
Notwithstanding that Islam WAS mentioned in Cameron's speech, alongside extremism - to me the two components are different.
a) Integration etc., call it what you like,
b) the missing National Identity.
Our national identity is constantly changing - in this small town, we have three Polish shops, several Indian restaurants, several Chinese restaurants, Thai food outlets, Aldi/LIDL (can't get much more Germanic than that), Netto (Swedish), etc etc. They all contribute to multiculturalism in this town, and all the locals use them - so here it's working in terms of assimilation, but people still talk about "the foreigners". How would anyone determine that all these groups in our small town should all assume this National Identity (apart from all speaking English, which I think should be a given)?
The existing Test about the UK which some immigrants have to take before they will be admitted to the country contains questions which I doubt a lot of the locals here would be able to answer (and I include me in that), including memorable British dates and laws and names of past Prime Ministers. How relevant are those things to current British way of life to someone coming in from say Somalia? Does knowing those facts, give them our National Identity?
I'm just brainstorming here, I have no idea what's in Cameron's mind or what suggestions will now fall out from his speech in Munich yesterday!