Is Edinburgh well-known internationally?

Yes.
Gordon Brown has done ok afterwards, Darwin did ok aswell.
Although Darwin did actually drop out, and then went on a journey cause he was bored and he was a lazy bum sat on his arse watching telly- well obv not watching telly.
But yeah
Edinburgh is well known

I know it's prestigious and well known in the UK (and now i know a few famous alumni lol) but is the fact that it has been falling a lot in the league tables a worry? it's gone from 3rd best to 18th in like 4 years, a degree from Edinburgh might basically become not exactly worthless but it may carry far less weight in the future- is this a cause for concern? would i be better off in a university like say Warwick which has basically been getting better and better...i'm so confused

you have to look at course rankings. The overall rankings vary every year (well course rankings too, but they are more stable). Plus, the overall rankings do not have much relevance to your career in many cases. For instance, suppose your university is ranked 5th overall, but 19th for your course, would you still choose that university, when you have another option that is ranked say, 11th overall, but 4th for your course?

Yh i see what you mean, at the end of the day it's the course that matters i guess seeing as you will be studying it for 3/4years

If your course is directly linked to your future professions (e.g. Law, Medicine, etc), your course reputation will affect your employability. I mean, how are the overall rankings even valid when you're being evaluated as a candidate for jobs? when about 1/4 or 1/3 of the universities in the overall rankings do not even offer your course, and the most important thing is how well and how much you know about your subject rather than your university's superficial overall rank?
But i think if your course is something like say, English lit, I don't think your university's course ranking wouldn matter much i think.
Depends on which course we're talking about basically.

starting to understand now- but in my case because i'm studyng history its not really about the course (unless go into history postgrad or something history related)- that's why i asked the question about it being nternationally well known, im just stuck between Edinburgh and warwick (i'd say UCL too if i could get the grades!)

Congrats on your offers so far! Edinburgh and Warwick are all top-class!
I'd normally suggest you go to Warwick, as it's ranked much much higher than Edinburgh for History. BUT since you aren't going into history postgrad or anything like that, overall reputation is more important. It's a difficult situation. Edinburgh is more recognized internationally, but Warwick is one of the best domestically. If you're gonna get a job outside the UK, you should prob go for Edinburgh and if you're gonna stay in the UK, then Warwick.
I think you should visit them and take the 'feel' of the universities into consideration as well, since you're gonna spend the next few years of your life in one of them.
Wait for UCL though. UCL would be the best option. It's recognized as one of the best domestically and internationally.

Put it this way - so far, i've only had 3 British lecturers. The rest have been American. :P

really? are a lot of the students americans too (i'd have thought they'd be scottish)

Most of the students are British, but there are quite a few international students, about 15 % of the whole undergraduate student population, I think.

really? are a lot of the students americans too (i'd have thought they'd be scottish)