I’m a co-author on a report written about Brexit and Equality Rights by the Oxford Human Rights Hub. I was the research assistant so wrote the first drafts of it (which the professors then worked on, so more credit to them!), as well as doing the formatting and sending loads of emails. But many of my words are in it.
The summary is: most of our equality protection is closely linked to EU law, so when that goes our equality protection will be quite weak, as we don’t have a right to it or even our own constitution. The current approach in the EU Withdrawal Bill is to give government ministers the power to amend law that is currently EU law… So whereas usually it would need parliament to legislate, now a single government minister can make it. There’s a lot of important law within the scope of ‘EU law’ that could be amended, including many aspects of equality law… and there are no safeguards based on human rights or equality rights. Which is pretty shocking. So equality rights really are threatened.