An incident of alleged illegal hunting in Somerset is under investigation by a wildlife crime officer.
Police say the incident is alleged to have happened near Chard.
At Wells Market Place around 4,000 people gathered with the Mendip Farmer's Hunt. There was one reported assault of an anti-hunt protester.
"We have had a small number of crimes reported to us which will be fully investigated," said Assistant Chief Constable Rod Hansen.
Avon and Somerset police said 20 hunt-related events were held in the force area on Saturday.
"It is early days, but Saturday was a promising start for what is completely new legislation for us all," said Mr Hansen.
In Wiltshire four men were arrested at 0400 GMT on Saturday in what are believed to be the first arrests under the new hunting legislation.
The men were found on an unclassified road near Malmesbury, with four dogs and the carcass of a hare.
A 53-year-old from Ireland and three men, aged 31, 32 and 33, from South Wales, were arrested on suspicion of hunting with dogs.
The four have now been released on police bail pending further inquiries.
The men are also being investigated over possible firearms offences relating to a modified air rifle and possible offensive weapons charges.
Wiltshire Police spokesman Dave Taylor said: "We would stress that they were nothing to do with any of the organised hunts."
The Countryside Alliance reports around 12 foxes were shot in the West region on Saturday.
It says the foxes were killed within the terms of the ban either by being flushed to guns, or flushed from their earth to protect game birds.
Although hunting with dogs is now a criminal offence, exercising hounds, chasing a scent trail, and flushing out foxes to be shot are still legal.