Wa Alaykum Assalaam,
Is it really too late to apply? Have you tried UCAS Extra? That's basically if you don't have any offers or rejected them all, you can apply for courses with vacancies, but you can only apply for one at a time. You have until July to use this service. You can check the list of courses on the UCAS website which participate in this - they should have a little cross next to them. Before rejecting anything - you can contact the universities to find out if they will consider you in the first place.
Then there's Clearing - find out if it's an option by phoning the universities and asking whether they usually have spaces and whether they might accept you if you used it.
Before doing anything however, make sure you know what you are going into (which it sounds like you do). It would be risky to reject all those offers for something that is not guaranteed.
Another option is to find out whether it's possible to do one year of the Law & Int Relations degree, then transferring to the other course somehow. It could be that the first years are very similar and thus transfer a possibility.
The most important thing is to make Istikharah
before you do anything. Then after seeking the advice of people you trust, make a decision and place your trust in Allaah (swt).
I hope that helps Insha'Allaah,