More than 258,700 people have added their name to the e-petition since it was started in August 2012 and it is still gathering signatures. It will remain open until September 7.
It has now surpassed the previous most-signed e-petition which related to the London Riots. That attracted 258,270 names and is now closed.
The Government has said the badger cull is necessary to prevent the spread of bovine tuberculosis (TB) by badgers.
But the e-petition argues in favour of a more sustainable and humane solution, including a vaccination programme for badgers and cattle.
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