The Acaeum has a page devoted to the foreign editions of the Holmes Basic Set, noting four UK printings published by Games Workshop, and one Australian printing (rulebook only). Acaeum member dwarf has shown me evidence of a 5th UK printing with prices missing from the product list on the back cover. The text otherwise corresponds to the US "2nd Edition, Nov 1978".
The first two UK printings are especially noteworthy for having completely different artwork (cover by John Blanche, interior work by Fangorn). This Dragonsfoot thread has a comparison of the UK artwork with the original. Many, but not all, of the pieces show the same subject matter, but re-drawn by Fangorn. An interesting sidenote is that the Fiend Folio contains a full-page artwork by Fangorn that also looks like it could be a redone cover from US Holmes Basic rulebook (wizard and warrior facing off against a dragon). Possibly Fangorn executed this piece at the same time, but the John Blanche art was used instead and the Fangorn's ended up in the FF. The original art for Blanche's cover can be seen here.
In a 2001 interview, Gary Gygax was asked about the UK version, and responded:
"Yes, I saw the work, and I approved. Ian [Livingstone] and Steve [Jackson of Games Workshop] convinced me that their audience didn't like the illustrations used in American versions of the game, so I gave them the okay to produce their own. I had a copy of the Basic Set rules, but it was lost when Lorraine Williams took over TSR..."
The UK version was available as of December 1977, as evidenced by a photo from Games Day III (Dec 17, 1977), published in White Dwarf #5, which shows Don Turnbull and Bill Howard holding copies of the new rulebook.
An early review of the UK rulebook appeared in January 1978 in Gallimaufry #12, a Diplomacy zine out of the UK that ran from 1976-1979, edited by Steve Doubleday.
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here on Dragonsfoot.
A photo from Games Day III (17 December 1977) that appeared in White Dwarf #5 (Feb/March '78), pg 15.
From left: Bill Howard, Don Turnbull (pointing down at UK Basic rulebook), Tony Ball and Rob Thomasson.