This is no simple answer to this question because Uyghur has two meanings: an ethnic group that became self-conscious in the 1920s and a tribal confederation in the 8th and 9th centuries AD. Whether they are the same thing is highly contentious. There certainly have always been Turkic-speaking peoples in the oasis towns of the Tarim basin between those two periods, and they have interacted with Arabs, British, Dungans, Han Chinese, Hui Chinese, Kazakhs, Kyrgyz, Mongols (both Dzungar/Oirat and Khalkha), Persians/Iranians, Russians, Tibetans, Uzbeks.... and I've surely missed a few. This is the crossroads of Asia and any answer is going to be complex with lots of caveats.

My usual analogy here is pointing out that Romanians are clearly linked to Romans (Romanian is a Romance, i.e. Latin-based, language) but we can't simply say "Romanians are Romans". You appear to be an Australian, so I'm not sure whether that analogy is helpful at all....!

Source: David John Brophy Tending to Unite: The Origins of Uyghur Nationalism (http://ucblibraries.colorado.edu/ebooks/Dissertation--3462443.pdf). I've read about a third of this and it's not for the faint-hearted - you'll need to be comfortable with skipping over snippets in four languages from as many scripts..... All part of the fun of Central Asian history!