From Vancouver BC to England via sea container, (2 years ago) $800.00 CDN this thru a common carrier time was not an issue, so it took over 2 months--- Evergreen is a container carrier that hits every stop between here and everywhere, other wise I can ship to Italy for $2000.00 CDN, delivery under a month.
Check any Brit publication that includes antique/classic cars there are many shipping company's/brokers listed
As to taxes you will probably have to pay the Inland Revenue the VAt tax on purchase price if you are shipping your bike to ride
you will probably have to pay port taxes go on line Google "Inland Revenue" and search for the costs
Good Luck!!!!!!!!!!!!!!!!!