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I think that you can find the answer to this question in the lines immediately following the one that says he is starting to sweat. There, Orwell tells us that Winston is afraid of the girl. He keeps seeing her around and, in that society, he naturally thinks that she is somehow spying on him. In our society, he might think she was interested in him (which she is). But in his society, personal relationships just don't happen. So if someone seems to be watching you, they are probably spying on you for the Party.
You can see this fear of his in the following passage:
Why was she watching him? Why did she keep following him about? Unfortunately he could not remember whether she had already been at the table when he arrived, or had come there afterwards.
If you keep going a bit down from there, you will see that he says that he thinks that she is some amateur spy. He says that they are the most dangerous kind.
Winston thinks the dark-haired girl is a spy that was sent out by the Party to watch him. He is really nervous because he suspects that that the government is going to punish him if Winston does something wrong.
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