When Exeter based Jersey European were looking to re-brand in 2000 they did a survey on market perceptions of current airline performance. Among the the usual suspects they inserted British European, a name that morphed into British Airways from the the early days of BEA's 1971 merger with BOAC. Despite the fact that the name hadn't operated or existed since its last remnant BEA Airtours became British Airtours in 1974, British European came out as an excellent performer. That clinched the decision. Jersey European became British European on 1st April 2000 and the old BE flight designator was soon also acquired. 2002 then saw a complete relaunch and image change. FlyBE was born.
Footnote: There were no legal obstacles to Jersey European adopting the British European title. Although British Airways had retained the registration of the British European Airways name it had taken out no protection for British European on its own.