Welcoming the recent suggestion from Richard Caborn, the Planning Minister, that Leylandii hedges might be required to have planning permission, the motion suggested even more extreme measures to deal with "this increasing menace" - criminal sanctions.
Sponsored by Lynne Jones, Labour MP for Birmingham Selly Oak, the motion said that while "a key element in many of the most distressing disputes over high hedges is unsocial behaviour and harassment", the existing Crime and Disorder Bill might provide a means of tackling the problem.
However it was dealt with, the MPs wanted "effective measures to tackle the vindictive impulses of those who insist on allowing their hedges to reach monstrous heights, with the main purposes of inflicting misery on their neighbours."
One of Dr Jones's constituents is Michael Jones, who spent 18 years and pounds 100,000 in legal fees on a dispute with a neighbour over a 26-foot Leylandii hedge.
Mr Jones, who was allowed to prune back the offending hedge to a height of 12ft, has since set up a support group, called Hedgeline.
Dr Jones has won the backing for her motion from signatories stretching from Ken Livingstone on the Labour Left through to David Amess on the Thatcherite Right of the Conservative Party.
Dr Jones told The Independent that she did not want to stop people growing Leylandii hedges, or any other kind of large hedge. "It's only when it forms some kind of anti-social or oppressive behaviour," she added, "then, the fact that there is some kind of sanction might help to ease matters, and in most cases help to solve the problem."