Realistically, Winston Churchill couldn’t have offered any worthy advice as concerns the Internet (if indeed he actually made any statement about the Internet, which I highly doubt) as such came about essentially after his days.
Winston Churchill suffered a series of strokes (in 1949 – age 75 & 1953 – age 79) making his speech impediment all the more difficult to deal with and slowing him down physically, causing him to retire as Prime Minister in 1955 at age 81. Churchill suffered another mild stroke in December of 1956 at age 82. By 1959, and 85 years old, he could only enter the House of Commons in a wheelchair. As his mental and physical faculties decayed further he began to lose his long battle with depression. It was speculated that Churchill was suffering from Alzheimer’s disease in his last years though others contributed his decline to the series of strokes he suffered over the years. Hence, his mental faculties were already in decline long before the earliest development of the so-called “Internet” in the early 60's where it was more concept than an actual world wide web.
Winston Churchill suffered a severe stroke on January 15, 1965 and died nine days later on January 24, 1965 at 90 years of age. Though he tried to remain active in public life, he remained more the recluse per his increasingly more silent latter years, so it’s not likely that Churchill ever made any statement concerning the “Internet”, as such was of little consequence back then and his faculties were greatly diminished by the time the earliest stages of Internet development had come about. Since there was virtually no general populous usage of the early Internet (barely affordable personal computers had only come into existence by the latter 1970’s attributable to the rise of the first commercially available general purpose 8-bit microprocessor chip, the 40-pin Intel 8080 in 1974), most people wouldn’t have had a clue as to what an “Internet” was hence, a statement by Churchill concerning the Internet would have been essentially pointless.