[acatnamedjoe]

"Firing" is becoming a bit more common in Britain, but still sounds like an Americanism to my British ears.

I would use "sacking" for performance related termination, and "losing ones job" in all other cases. I suspect BBC would use the same.

[cjrp]

"Made redundant" is another term for the latter.

[ghaff]

Which, at least in American English, comes across like corporate jargon/weasel words. Lost their job is literally true and would probably take a bunch more words to describe the precise reasons.

[hackeraccount]

Synergized is the term I typically hear.