And the answer is… Ofrex!
This mark was the business-oriented side of Rexel (possibly a portmanteau of Office and Rexel?) which had been established in 1939 by George Drexler, originally from Prague.
The Ofrex company itself has been around since at least 1950, with Rexel a retail subsidiary. Most of the mechanical pencils I know of (and there were many) were sold under the Ofrex brand, but there are a few Rexel examples.
In 1980, Ofrex acquired Cumberland Graphics and Cumberland Pencils, including their famous Keswick factory. The following year, Ofrex itself was acquired by Gallaher Ltd, a subsidiary of American Brands Inc, which then shifted focus to the Rexel name. In 1987 the ACCO office supply company was also acquired, and merged with Ofrex/Rexel in 1992 to form ACCO Europe, with Rexel remaining a sub-brand. Rexel now deals primarily in paper shredders, but still sells some general office supplies - sadly no pencils - while the Ofrex brand seems to have been retired.
A handy PDF timeline of the companies can be found here.
The Ofrex 0.5 mm pencil itself is quite an unusual beast, with no other markings beyond those visible in the photo. As mentioned earlier, it has no clip and the central part of the barrel is hexagonal to prevent rolling. The rounded “tail” section gives it an oddly symmetrical look, but the weight distribution is quite nose-heavy, with the balance point around the middle of the word “OFREX”.
The nose cone unscrews to reveal a brass clutch, while the end cap contains a short pink eraser with embedded lead-clearing wire. I can’t disassemble the pencil any further to see the lead tube itself. The smooth metal grip appears to be somehow bonded to the other parts.
I separately acquired a box of Ofrex 0.5 mm lead refills, which I assume are from the same period. The design of the lead boxes is just as quirky as that of the pencil itself, not to mention being quite hefty. The concave sides seem possibly intended to double as a pencil rest, while the internal circular cavity of the box is huge, able to hold up to 72 leads, six times more than the 12 supplied. Unlike the pencil, the lead containers state very clearly that they are from Japan.
This is the only example of the Ofrex pencil I have come across. I assume it was made for them by another company (possibly Japanese), in the same way as the Derwent Precision seems to be a rebranded Deli pencil. As always, any new information would be very welcome.
