Jon:
Contact an airline that offers shipping services for motorcycles. If your destination is Canada, that would include both Air Canada and WestJet. There are lengthy discussions here on the HUBB about the services that both of these carriers offer - have a look in the
Trip Transport section here on the HUBB.
It's not necessary to crate the motorcycle if you are shipping it with an airline that offers motorcycle shipping services - just show up with less than 1/4 of a tank of fuel. The air freight handler for the airline will strap the motorcycle down on a pallet, much the same as you do when you travel by ferry.
I've shipped my moto from Canada to Europe and vv several times, never had any problems, never needed to crate it.
FWIW, even though you are (presumably) based in the UK, you might find it cheaper overall to ship out of France or Netherlands to Canada... Heathrow is one of the most expensive airports in the world to ship in and out of. So check the prices for shipping out of continental airports that are close to you and do the math.
So far as arriving in Canada is concerned, you don't need a carnet or any fancy import paperwork. Just ensure that you have the ownership & registration documents and proof of insurance for Canada (if the insurance is valid in Canada, it will also be valid in all 50 states in the USA).
It is very important that the motorcycle is perfectly (and I mean
PERFECTLY) clean and has no evidence at all of bug splats, mud under the fenders or on the tires, etc. This is because Canada Customs biggest concern will be the risk of importing an insect egg or a seed that is not native to Canada. Get it steam-cleaned a few days before shipping, then detail it yourself, and don't ride it to the airport if it is raining that day.
Michael
PS: An alternative is to contact a company that specializes in shipping motorcycles by air between Europe and North America.
Motorcycle Express is such a company. I have used them in the past, they are very experienced, very professional, and I can recommend them based on my experience.