The rejection rate peaked for 2020 near the end of the year - when France shut its borders to British truckers for 48 hours in a renewed Covid scare.
Truckers now must fill out customs forms and undergo checks. Authorities becoming stricter and firms bailing out of contracts.
They look for better rates on the spot market, said Stephan Sieber, chief executive of Transporeon, which tracks the figures.
German state-owned DB Schenker, a major logistics company, suspended deliveries to Britain due to post-Brexit red tape.