In the introduction to his Collected Short Stories, Forster said "The Machine Stops" was
a reaction to one of the earlier heavens of H. G. Wells.
"The Machine Stops" was published in 1909, which gives a later limit as to which of Wells' stories or novels he could have been responding to. Someone more familiar with H. G. Wells' work may have a more definite answer, but my suspicion is that it might have been When the Sleeper Wakes, a story originally published in 1898-99 and republished in a revised form as The Sleeper Awakes in 1910. When the Sleeper Wakes features devices called Babble Machines, which are used to spread propaganda and subdue the population:
so far as the more prosperous classes were concerned, in all the more comfortable private apartments of the city were fixed Babble Machines that would speak directly a lever was pulled. The tenant of the apartment could connect this with the cables of any of the great News Syndicates that he preferred.
If I'm right, Forster was probably being ironic or semi-ironic by describing this as one of Wells' "heavens", since the future society in When the Sleeper Wakes is not exactly a utopia.