A good chuckle reading this thread.
Yes, Bealine is still used by the BA maintenance tugs at Heathrow - not uncommon to hear "Bealine Papa Echo" or similar requesting a re-position of an evening. Luckily for the residents nearby, it's an A319 going for maintenance nowadays instead of a Trident 1 going for engine runs.
Trying to choose an acceptable callsign which remains available for a new airline isn't easy. I seem to recall we tried everything we could think of to inject some humour but failed miserably.
"Thunderbird" was already taken by an airline in Canada. Our aim to generate a laugh every time by calling for push-start as "Thunderbird One" failed miserably.
Next request was for "Nighthawk" as a run of faux-French accents calling 'allo 'allo to London would have brightened up the morning. That was a no-go too, for reasons I can't recall.
We tried all sorts and by a process of elimination ended up with something so mundane that I now can't even remember what it was. Efforts to brighten up the airwaves well and truly grounded.