I'm not an immigration lawyer but as I understand it: having been born in the UK as the child of Bangladeshi parents who were living here legally she was entitled to British citizenship, but she wasn't British automatically. They would have had to apply for it. As such, the politicians were able to take it away.

This is quite a recent change in the law. Prior to 2014 they could only strip citizenship if you applied and received it without having a right to it (e.g. if you were born abroad to non-British parents). After 2014 naturalised citizens (like Begum) were also liable.

I do think it is a bad law and she is being treated disgracefully. There's still hope the ECHR will sort it.