It's apocryphal, found in Bartlett's Book of Anecdotes etc. Levenson's book (which BTW has a lot more of interest beyond whatever I put in the blog post) cites two sources for this point:

• Richard Westfall, Never at Rest: A Biography of Isaac Newton (1980), p. 483

• A. Rupert Hall, Isaac Newton: Adventurer in Thought (1992), p. 231

I looked up both those books and both of them call it an anecdote.

Westfall:

> There is no way to pretend that Newton played a leading role in its deliberations. According to a story that rests solely on anecdotal authority , he spoke only once; feeling a draft, he asked an usher to close a window . It is not merely anecdotal that none of the surviving accounts of the Parliament contain any record of his participation in its debates. Only to a limited extent do we know where he stood on the great issues the Convention Parliament decided.

Hall:

> An anecdote records Newton's only utterance in the House of Commons: feeling a draught, he requested that a window be closed. However, anecdote may be erroneous. Since Newton asked leave to bring in a Bill to confirm the charters and privileges of the University of Cambridge, he must have made some remarks, however terse.