Don't worry about it, once you get past the top 200, which all of those universities are in, employers across the world don't really care and there's a fairly negligible quality difference between them.
Edinburgh loses out in the UK league tables because of the student satisfaction rating and slightly lower research rating. Low student satisfaction scores can be very difficult to judge as there are a myriad of things which can scar a person's perception at the end of their course when they fill in the National Student Survey. Research rating is mostly irrelevant for undergrad/postgrad taught as while the research you do in your dissertation is an important part of uni life, it allows means basically nothing to anyone who isn't in a very small field. It's also pretty irrelevant for postgrad research too because a uni can be absolutely stellar at one tiny subject and useless at the rest, if your research is in that tiny subject then you'll be treated like how most people imagine Oxbridge grads are even if the university you graduated from doesn't even appear in the top 2000. Edinburgh is really, really good for AI, so this is relevant to them.
I would consider travel links too as an international student. Manchester will likely have the best flight options though Warwick (via Birmingham airport) and Edinburgh won't be far behind. Manchester is definitely the best by rail though and has a very good public transport system.