The couple are moving out of the upmarket area of Belsize Park in North London after a series of arguments with their neighbours, who are upset by constant modifications to their property.
A local told the Daily Star newspaper: ''We have had years of their building works. They have taken down trees so they can park their flash cars in the driveway and they put a huge swimming pool in the back garden.''
Another neighbour added: ''The trouble is that it will probably be a similar sort that moves in and we'll have this all over again.''
'Iron Man 3' actress Gwyneth and Coldplay singer Chris - who have Apple, nine, and Moses, seven, together - bought their home ten years ago for £2.5 million from actress Kate Winslet. They then bought the neighbouring property for £3.1 million as well as another house on the other side and combined all three to make a huge 33-room mansion.
They are thought to be selling the house and downsizing because they don't spend much time there after relocating to Los Angeles last year.
A source added: ''They are looking at flats in Regents' Park to use as a bolthole when they visit London.''
The power couple also have a warehouse penthouse in New York which they bought in 2007 for a reported £3 million.
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