You would be surprised. I have a fair few fellow students who speak English well enough to hold basic conversations but the moment you need to talk about more than the weather they lack the understanding of the language to put the sentences together (like someone who can piece together code suddenly being asked to synthesize a new program from scratch). A few fair better in technical subjects but at least for one English university, this doesn't appear to be a barrier.

(As an aside, I had a pair of Portuguese TAs who spoke very good English, but had a slight issue with the letters of the alphabet. And a couple of the English letters share names with different Portuguese ones which made for interesting Elementary Logic tutorials.)