Stephanie and Alex Birch, of Gorse Bank Farm in Baslow, fear they may have to slaughter their 30 cows and calves after a member of the public made a complaint to the Health and Safety Executive (HSE).
The HSE said it had not ordered the slaughter of the cattle and that an investigation was ongoing.
Mrs Birch said the member of the public complained to the HSE after he went on to their moorland with his dog and was approached by one of their cows.
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She added that all the HSE had told her and her husband was that ‘the cow approached him (the complainant) and pinned him against a wall’.
Mrs Birch said: “In our eyes we have not been given any evidence that pertains to any of the herd being aggressive.
“We think we have a safe herd.
“If you know cows you’ll know they’ll often walk up to you, especially if you have a dog - if you’re not used to that then you might back up and end up against a wall - but I don’t think I’ve ever known a cow to be aggressive and to pin someone against a wall.”
Mrs Birch said that the HSE suggested moving or segregating the cattle.
However, she added that these were not viable options for a number of reasons including significant costs, planning consent challenges and time.
Mrs Birch said: “We don’t want to have to slaughter an entire herd of cattle that don’t sound like they have actually been aggressive.
“We’re annoyed and devastated.”
A HSE spokesperson said: “HSE officials have not ordered the slaughter of cattle at this farm. Our investigation into this incident remains ongoing.”
A HSE information sheet states: “HSE regularly investigates incidents involving cattle and members of the public in England and Wales.
“Some of these result in death or serious injuries.
“Almost all of these incidents are in fields and enclosed areas. Many other incidents occur but are not reported to or investigated by HSE.
“The two most common factors in these incidents are cows with calves and walkers with dogs.”