Members of the National Trust have voted to relax their rules on hunting on Exmoor.
The law makes it illegal to hunt with dogs in England and Wales
If the vote is adopted as trust policy, hunts will be able to follow sick or injured deer on to their land to kill the animal.
Trust members voted to allow hunting of stags at the Holnicote Estate, which forms much of Exmoor.
The results at the annual general meeting in Cheltenham were 12,768 in favour of the ban, 20,188 against.
Sir William Proby, trust Chairman, said: "We are grateful to our members in making their views felt during an impassioned and helpful debate.
"The board of trustees will take the outcome of this debate into consideration in assessing the issue of exempt hunting, but our approach to deer management will continue to be driven first and foremost by practical considerations of animal welfare."
Protesters from the League Against Cruel Sports gathered outside the meeting at the town's racecourse in an unsuccessful attempt to persuade delegates to vote against allowing injured animals to be hunted.
The trust banned stag hunts about 10 years ago and hunting with dogs became illegal in 2005.
The fox hunting season began on Saturday, with thousands of enthusiasts setting out on foot and horseback following packs of hounds.