It's most probably parking provided by the local council close to a football pitch or pitches. For the use of the players, supporters etc...

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Note added at 9 mins (2006-12-17 13:20:20 GMT)
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etc!

Such allocation is usually only for the time periods during and around game time.

Your question clearly indicates: "service provided by the council", so I don't think that the answer is restrictions.

The parking zone mentioned by Kim is to KEEP THE FOOTBALL FANS AWAY from the nearby residential areas, but it is not the solution for the fans, rather the opposite.

The solution is DESIGNATED PARKING (special parking lots) and PARK-and-RIDE, which is set up by the council especially for that purpose, to be used on the days when matches are held.

KC Stadium, Hull
...straight off the motorway and onto park and ride which takes you to the ground. www.sportnetwork.net/main/s37/st94566.htm

Ground: Molineux
Wolverhampton Wanderers (Wolves)
As you approach the 2nd set of lights look for the signs for football parking. new.pinkun.com/content/NCFC/AwayGuide/Wolves.aspx

Brentford:
....you will see a sign further down on your right for football parking. www.bias.org.uk/away_game.php?id=17

Britannia Stadium, Stoke on Trent, (Stoke City FC)
...turn into Heron Cross and find the football parking there.
travel.cpfc.org/docs/1141945090,10625,.php3

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Note added at 1 day1 hr (2006-12-18 14:46:31 GMT)
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In the UK the term "football parking" means vehicles parked by people attending matches, or parking facilities provided for that purpose.
The quotes above all refer to where to find "football parking", how to get there, etc. If there isn't enough parking facility by the grounds, most councils provide alternative parking, especially if there are existing parking restrictions in the surrounding area, which is usually the case.

In the case of Liverpool, there are no everyday parking restrictions around the grounds, therefore the council brought in the special measure you quoted; for match days to help residents.
This was the first UK website to come up when googleing the subject, but that doesn't mean, that this is the usual solution, for the above mentioned reasons: the expression "football parking" here (UK) means fans parking, and big football stadiums are more often than not in an area, where there is a parking restriction in force anyway, so the council doesn't have to bother to introduce them for that purpose, but because of that, they have to provide alternative parking, if they want their local football team to flourish.