Devon and Cornwall Police have admitted that they will be "piggy in the middle" between hunt supporters and opponents when the ban comes into force.
Hunting with dogs will be banned from Friday
Assistant Chief Constable Richard Stowe said the force was "very aware" of the sensitivity of the issue of banning hunting with dogs in England and Wales.
He also added that it would be difficult to distinguish between what was legal and illegal hunting.
Hunt supporters say they will continue efforts to overturn the ban.
Devon and Cornwall Police said that the ban, which comes into force on Friday, would pose a "significant threat" to the force.
Richard Stowe said: "We're a large rural police force, we've rural communities that have strong views, which does put the police as 'piggy in the middle'.
"It will cause a great strain for any force, but especially one as rural as ours.
"The ban has many complex technicalities. We've designated it as a wildlife crime, and we will get used to the new law and enforce it.
"But things like violent crime, burglary, vehicle theft will be higher priorities than hunting."
Chris Deacon of the League Against Cruel Sports said the force had been present at hunts before at its request. He said that meant it should not affect it being at hunts again.
He said: "The police have had the capacity to attend hunts in the past, so we can't see why that would be any different in the future."
The Countryside Alliance had its latest legal bid thwarted when three Appeal Court judges rejected its argument that the Hunting Act was unlawful on Wednesday.
It had claimed that the 1949 Parliament Act, which MPs used to introduce the Hunting Act after House of Lords opposition, was invalid.
The campaign group said it would now take its case to the House of Lords and to the European Court of Human Rights.
The alliance has said about 50,000 people are prepared to break the ban and continue hunting "in the full knowledge they will be arrested".