Has there ever been a fictional plot, either book or movie, that
involved arranging for Big Ben to chime early/late or or with the
incorrect number of chimes, as a form of communication from the
government?

Indeed! In the James Bond movie "Thunderball" (1965) the British
government agrees to pay an exorbitant ransom to SPECTRE, and they
arrange for Big Ben to chime 7 times at 6pm to signal their acceptance
of the terms. In the conference room where all the "OO" agents from
Europe are gathered, a tape recording is played and they listen to
SPECTRE's demand. SPECTRE states that it has hijacked two atomic bombs
from a Vulcan aircraft during a NATO training exercise, and unless a
ransom of 100 million pounds is paid, it will launch a nuclear attack
on a major city. To signal its acceptance of the terms the British
government arranges for Big Ben to strike 7 times at 6pm, as
instructed on the tape.
  
  
"Big Ben is considered one of the most accurate clocks in the world.
However, In the James Bond movie Thunderball, S.P.E.C.T.R.E. demanded
that the British government pay a ransom of 100 milion pounds to
prevent an attack on a major city. To signal their acceptance of these
terms, the government was to arrange for Big Ben to strike 7 times at
the hour of 6 p.m!"
  
http://www.seeing-london-by-underground.com/Big-Ben-pictures.html
  
  
You can read more details about the plot here:
  
http://www.geocities.com/Hollywood/Lot/7924/thunder.html
 
   
"Thunderball" DVD from Amazon
http://www.amazon.co.uk/exec/obidos/ASIN/B00004SH4R/026-2882288-1952448
 
"Thunderball" book from Amazon
http://www.amazon.co.uk/exec/obidos/ASIN/0141002999/026-2882288-1952448
 
  
   
I hope this helps.
  
  
Jackburton
   
   
(Thanks to needsomeinfo-ga for jogging my memory!)

a gimme from a comment, but I left the question standing so that a
researcher could claim. Comprehensive answer - thanks for the
additional links.

HI,
I seem to remember a story about Big Ben  (but maybe it was a much
smaller bell somewhere else) starting to ring 13 times at midnight. 
The story was, that someone was firing a rifle at it to make the 13th
stroke.  Of course, a bullet striking that large bell would probably
only make a "plink" instead of a "gong",
hence my suspicion that the story was about some church with a tinny little bell.

But did you get the news:  Big Ben went on strike (heh, heh!) Friday
night or Saturday morning, well the clock did, stopping for and hour
and twenty minutes.
That just isn't supposed to happen; it is as though time has been
suspended in the whole realm  - but it isn't what it used to be
either.

It's true, came through on a banner on a German TV new channel.

Maybe it was suffering from heat stroke?

That news story is what prompted my question. It reminded me of some
plot, but I can't remember it.

Odd concidences...I just happen to watch this movie today for the
first time.  It was a James Bond movie (Sean Connery) Thunderball. 
The plot was something like give us money or we'll blow something up
and tell us you agree by making Big Ben chime 7 times at 6 o'clock. 
I'm sure if you google the name of the movie and Big Ben you can get
more info.