The Eastman name wasn't used at all in the UK, it's Kodak Ltd. Tha main UK Harrow factory was second in size to Rochester and had it's own Research facilities.
UK products wouldn't be identical but rather close, Tri-X varied in speed & behaviour with different dev times depending on whether it was made by Eastman Kodak, Kodak Canada or Kodak UK, and just prior to WWII it was made in Kodak;s Hungarian plant (later to become Forte).
So Eastman Bromide = Kodak Bromide approx. remember both research facilities were run by former Wratten chemists - Mees was Wratten's MD and founded Rochester Research and Harrow.
The Gelatins could vary, they weren't understood fully for years. Kodak in the UK also had an alarming habit of changing the products there was little consistent evolution like Ilford & Agfa, and they had a smaller market share.
In another thread today I mentioned how Kodak had a re-branding spree in the 20's & 30's in the UK adding Kod to Kodesko,
Here a starter Kothena, Kodesko, Kodatone, Kodura, Kodascpe (projector), Kodachrome, Kodatol (DK20), Kodinol (Rodinol type dev), Kodurol (glycine), Then silly names like Dolmi - amidol
They seem to have been dopoped by the late 30's due to confion
Remember as well that Kodak like US companies today bought others for their products, which is why Kodak develoers are illogically spaced and no pattern unlike Ilford & Agfa,
Papers came from Nepera, Cadett & Neal and Wratten & Wainwright of course as well as US acquisitions.
Ian