A Cooksley woodworking machines catalogue is available
Once a very well-known and respected makersof wood-machinery, Cooksley was founded in 1896 and based in Kingston-upon-Thames. By 1961 thay had 150 workers making a wide variety of professional woodworking equipment including a small but robust woodworking lathe that appears to have been built in two versions: one was identical in design and configuration the Harrison "Jubilee" (and, judging by the screwed-on cast-aluminium Cooksley badge was simply that lathe re-branded) while the other, badged as the "Handy" was, oddly, very similar in general construction but with a number of notable differences and almost certainly built by Cooksley themselves.
Both are now very rare: they were heavily built from fabricated steel plate on an underdrive plinth with the drive motor mounted on a vertically-adjustable plate. A large capacity bowl-turning attachment appears to have been a standard fitting and, like the Harrison Union Jubilee, could be had with a rack-driven carriage assembly for precision wood-turning or light metal-working jobs.
If you have a Cooksley wood lathe, the writer would be very interested to hear from you.