No person has any natural rights that can overwrite the personal rights of other people.
100% correct.
Even the women who "wear the burqa willingly" do so because of years of indoctrination, social pressure,
Problem is that many, if not most, choices people make are strongly influenced by indoctrination and social pressure, so this can't be the sole justification for state intervention.
and fear of physical abuse.
Then that should be dealt with as a criminal matter.
I will grant you a Muslim-majority country like Turkey may have justification for a ban on the burqua, because otherwise physical abuse and intense social pressure on women to wear it may be so widespread that it would be nearly impossible for the state to protect women who choose not to wear it, but in Western countries this is clearly not the case. Muslim women can choose to leave their husbands or even their entire immigrant community and keep custody of the children in Western countries, and it is within the power of the state to assist them in relocation and protect them from physical retaliation.
So while you may have an argument that state violations of women's right to choose to wear a burqua are necessary in Muslim countries to prevent much more widespread violations of women's rights NOT to wear a burqua, it is not necessary in the West-- there are options which are less invasive and ultimately more effective at the ultimate goal-- women's liberation.
Even Condell admits in the video above that if Britons had the guts to socially challenge the burqua there would be no need for a law. Well, if Britons (or anyone else) don't have the guts to challenge something they think is wrong, why the hell should the state pass invasive laws just to make things easier for people? It shouldn't-- there are thousands of ways to assist liberation of Muslim women in Western countries, both with and without the assistance of the state, that don't involve the implementation of new laws that regulate personal conduct which does not directly and immediately threaten the rights of another-- banning the burqua is a lazy, unnecessarily invasive, dangerous, and ultimately ineffective method for liberating Muslim women in Western countries. Wholesale bans on items or personal conduct normally are lazy, cowardly, and ineffective policy-- guns, hate speech, burquas, drugs-- these are all laws that come from people who have run out of ideas, courage or will to solve the problem effectively and in the least invasive manner possible.