Footage from hidden cameras revealed a string of cases in which the animals were attacked.
Researchers visiting the site also photographed dead calves left to rot outside.
One worker also appears to touch the animals in an “intimate area” on two different occasions, the witness claimed.
“Some of the most disturbing footage shows one worker touching two cows in intimate areas on two different occasions,” the investigator said. “The worker appears to be moving his hand up and down in a way that would suggest masturbation.”
At other times, employees carried out “excessive tail twisting” – causing pain – shouted and swore at the animals.
Mr Smith, whose farm is arable, said he had no input into the running of the dairy side of the business and derived no financial benefit from it.
The dairy division said disciplinary action had been taken against the workers.
The investigation was triggered when a member of the public spotted the decomposing body of a calf and raised the alarm.
Without knowing the link to Mr Smith, investigators say, they placed hidden cameras throughout the farm at St Osyth, near Clacton, and visited several times over two months earlier this year. They sent their findings to the Surge animal protection group, which campaigns against the dairy industry.
Ed Winters, co-director of Surge, said members were shocked by the brutality documented on the farm.
“Guy Smith travels and gives talks about animal welfare, whilst on his farm animals are being touched in intimate areas in a non-legal manner, punched, trapped in solitary confinement pens and verbally abused,” he said.
“This farm was just one of eight UK dairy farms featured in our larger Dismantle Dairy campaign, and on all eight dairy farms we found suffering and abuse that is hidden from the public.”
Surge, which reported the findings to the Animal and Plant Health Authority and the RSPCA, said there were numerous instances of violence or abuse.
Companies House documents identify Mr Smith as a director and one of five main shareholders of of Smith Farms (Clacton) Ltd, with 100 out of 500 shares. He describes himself on LinkedIn as owner.
In 2017, when asked by The Yorkshire Post about Brexit, he said: “As the secretary of state has said, we have the third-highest animal welfare standards in the world. British farmers are proud of their high standards and don’t want to see them watered down.”
The farm, which has hutches to separate young calves from one another, had an average of 25 employees in the year to January, filings show.
A signed affidavit shown to The Independent states the investigators entered the site “entirely lawfully”, that there was nothing to prevent entry, and that “nothing was damaged, forced, broken or interfered with”.
Mr Smith told The Independent: “I am aware there are allegations, relating to the treatment of dairy cows, made against employees of a company of which I am one of six directors.
“The allegations stem from illegally obtained video footage.
“I wish to make clear that I am not responsible in any way for the dairy side of the business and derive no financial benefit from it. In particular, I have no responsibility for the recruitment or training of staff and nor do I have any input into the manner in which that side of the business is run.”
Mr Smith, who has served for eight years on the NFU Council, added: “Animal welfare should be regarded as a priority and I have no doubt that those responsible for the dairy side of the business will immediately take all necessary steps so as to ensure the highest animal welfare standards are maintained going forwards.”
A spokesperson for the dairy division said: “The welfare of our dairy herd is our number one priority. We aim to uphold the highest standards of animal welfare and care and insist on the same high standards from everyone who works with us.
“We have taken immediate action in relation to the incidents shown (including disciplinary action) and have implemented a comprehensive retraining programme in our determination to ensure that any shortcomings in our systems and practices are addressed.
“Trespassers entered our farm unlawfully and secretly filmed many hours of footage over a period of 18 months. We regard this as a gross breach of privacy – of family members, children and staff members – and absolutely condemn it.”
The RSPCA said: “We were concerned to see this footage and we are looking into it further.”