Deer hunting with hounds may be allowed on National Trust sites as the best way to deal with sick and injured animals.
Hunts may be a humane way of dealing with sick deer, the NT says
Certain exemptions were granted as part of the 2004 act, which banned hunting with hounds in England and Wales.
Hunts are allowed to use two dogs to flush animals out of shelter, provided they are then shot quickly.
The trust is considering such methods for its property in the Quantock Hills and Exmoor where deer culls also take place at times to prevent land damage.
All hunting with dogs on National Trust land was outlawed in 1997 amid a campaign to persuade the government to make hunting with hounds illegal.
The Hunting Act, banning fox hunting, deer hunting and hare coursing with dogs, came into force in February 2005.
While the act permits two dogs to take part in a flushing out exercise - the number is still far fewer than would be found in a traditional hunting pack.
The League Against Cruel Sports condemned the use of dogs to flush out deer.
Mike Hobday, spokesman for the organisation, said: "Using dogs to force deer to run before they are shot will expose deer to needless cruelty.
"I am staggered that the National Trust would consider allowing this to happen.
"Badly injured deer on National Trust land should be stalked and shot as they are everywhere else in the UK - and certainly not chased."
A National Trust spokesman stressed it was not considering allowing fox hunting on its two pieces of land in the West Country.
"The proposal that is being looked at simply relates to sick and injured deer on National Trust land.
"It is a narrow way of trying to despatch them.
"At the moment it is not easy to isolate them and shoot them, so this may be a way of drawing out the sick deer and despatching them effectively and quickly."