I applied to 6 UK universities for a PhD programme in law. 3 of them rejected me around the same time, saying that they cannot provide supervision in my field. I have seen that there were relevant academics there who are willing to supervise students next year so I guess I was the problem... The other 3 universities (Queen Mary, Edinburgh and Nottingham) are taking really long, their webpages say it takes around 6-8 weeks but it has already been over 10 weeks now. One of them sent me an email 2 weeks ago saying that my documents has finally reached to law school from the admissions office but that was it. The other two still says "undecided" on their portal. Should I just give up and assume I am rejected?

I would contact them if I were you.

I would contact them and tell them you are eager to have a decision since time is running short.