The couple - who have lived in their Â£3.5 million North London property since 2004 - have been blasted for their "over the top" security measures after requesting planning permission to erect a 10-foot metal security barrier.
A neighbour told the Daily Telegraph newspaper: "It's rather over the top. Who cares who he is? You can't get round the side of the houses and into the gardens anyway. Other houses in the street are as much at risk of opportunist burglaries as his is. We don't ask for huge fences between our homes."
The couple's plans involve replacing a smaller wooden fence on top of a brick wall, for security reasons.
Chris and Gwyneth - who have five-year-old daughter Apple and three-year-old son Moses - are not the only famous faces to have annoyed their neighbours with troublesome outside structures.
Last year, Kate Moss received a letter from her local council after people in her London street complained about a stench from her drains and a crumbling garden wall.
One local resident said: "I think the wall is an accident waiting to happen. Young children walk past it every day on the way to school and it looks as if it could topple over at any time.
"There is a huge crack right through the middle of it and Kate needs to do something about it."
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