Ukraine is pretty easy. Not sure for Brits, but as stated above, you sould be able to get a visa at the border (at least Americans can...). Also, I believe that green card insurance covers Ukraine now, but check with your insurer. bring the originals of whatever bike rego docs you have, and probably an international drivers permit.
When you enter, get a "tourist" rather than a "transit" visa, because the "transit" visa requires that you exit at a particular border post, which can be a pain if you want flexibility.
Watch out for speed traps in Ukraine, cops can be a pain and kind of greedy.
What are you going to see in Ukraine? No offense to Ukrainians, but a lot of it is rather boring, with flat straight roads. South coast of Crimea is spectacular, but that's a long way...
It's really pretty easy!