Hunting with dogs in England and Wales became illegal at midnight.
However, hundreds of thousands of pro-hunt supporters have pledged to continue.
The lobby group, Countryside Alliance, said hunters would try to keep within the new law by drag hunting or flushing out foxes with shotguns.
Other supporters have indicated they will test the law, which they think is unworkable.
The Court of Appeal in London rejected a challenge to the ban on Wednesday.
Three appeal judges refused the Countryside Alliance's application for a stay, which would have blocked any potential criminal proceedings while the pro-hunt group petitioned the law lords for a hearing.
