Muslim women should demand civil marriages; these women shouldn't have just settled for a shari'ah marriage. Is this common amongst Muslims in the UK? To just live together and have children without even being legally married?
Here you'd normally go to an imam whose also a registered marriage celebrant to get married, and voila you're both legally and Islamically married, unless you ask him not to register your marriage (eg: if you're in a polygamous marriage and can only be legally married to one but want to be Islamically married to more).
Because the husband accepts the authority of the Sharia court and would thus only accept the divorce if the court ruled on it.
Otherwise he would just keep all the property and the woman would have to walk away with nothing (possibly not even her children), as happened to one of the women in the documentary.
After watching the documentary, I understand that some women have no choice but to go to these "courts" because they weren't legally married in the first place (hence not legally entitled to anything). I see how the man can get the property and material ppssessions but he couldn't possibly just take the children, could he? Unlike a house under his name, the kids aren't solely his by law.