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1.
Officially the worst train company in the UK. Their trains smell and are always late.

Often called "Worst Late Western"
"First Great Western? More like WORST LATE Western"
by Anonymous Passenger September 10, 2007
 
2.
"First Great Western" (FGW) is a slang term used in the UK to describe the worst levels of mediocrity and shameless arrogance.

Of a person: A person is "FGW" if they any or all of the following.
Rude, Surly, Arrogant, Lazy, Jobsworthy, Irritating, Unreliable or lacking in intellect.

Of a service: A service is "FGW" if it is all or most of the following:
Unreliable, Massively overpriced, Almost always late, cancelled, dirty or overcrowded.
I can't be arsed to work today, I'll chuck a First Great Western
by Richard Cheesed Off January 27, 2011