The phrase in "Hello World" is longer than those in "So Deep within You" and "Telescope (Mr. Galileo)," and it repeats more frequently. The song starts with it played four and a half times.
In "Hello World," it starts on a different pitch relative to the key than in "So Deep within You" and "Telescope (Mr. Galileo)," but the intervals are the same in all three (and the pitches of the first five notes are the same between "Hello World" and "So Deep within You").
(click the image to enlarge it)
(standard disclaimer that the notation may be wrong because I did it myself)
According to the liner notes in my Tremeloes collection (Silence Is Golden: The Very Best of the Tremeloes), "Hello World" was issued as a single in 1969. On the Threshold of a Dream - the album on which "So Deep within You" appears - was also released in 1969 (specifically, April). Apparently "So Deep within You" was the B-side to the "Never Comes the Day" single, released the same month. According to the liner notes for Into the Afterlife, "Telescope (Mr. Galileo)" was recorded in March 1968, although it wasn't released until Into the Afterlife in 2007.
So I have even fewer answers than I did when I wrote my original post. Now I have three songs that were all recorded and/or released within about a year and that all share the same phrase.