The main Morris texts which Tolkien admired were The Wood Beyond the World, The Well at the World's End, The House of the Wolfings and The Roots of the Mountains. I am not sure if he read News From Nowhere, but if he did (and why shouldn't he, if he was a fan?!), his thoughts have not been made public; from that I can only deduce that the first texts were the greater influence. This figures, as News From Nowhere is more political, and in some ways gets rid of the thorny point that Morris was a well known Socialist!
However, there is always a little thorn...
'Socialism' to Morris, and to Engels and to Marx was a very different thing to 'Socialism' in Tolkien's lifetime. And theory of Socialism is also a very different thing to practical applications of said theory. Tolkien indeed hated 'the machine' - but so did Morris, and Engels, and even Marx!
Jessica Yates, an expert on this, gave a paper on Morris & Tolkien at Birmingham 2006 - it's not yet available but in the latest Amon Hen it seems the TS are preparing to get a set of the papers out soon in the form of a 'commemorative booklet' - if it's anything like the Centenary conference proceedings it should be excellent.