Mr Woodcock, Labour leader on Cherwell District Council, spoke out after last week's vote on an amendment to the Agriculture Bill which farmers believe would have prevented future trade deals from allowing food into the UK not produced to the standards required of growers and processors within the UK.
Mr Woodcock's party and farmers' unions hope the House of Lords will reject the Bill and return it to the House of Commons.
Mr Woodcock said: "Banburyshire farmers would be understandably disappointed at Ms Prentis deciding that following the government whip is more important than solidarity with them.
"We've been told all along that environmental and consumer protections, previously enshrined by EU Law, will be maintained post-Brexit.
"But nothing is yet in place to ensure this in the event of future trade deals such as with the United States. Residents concerned about chlorinated US chicken on their plates will rightly be concerned. As will local farmers in danger of being undercut by producers over the Atlantic - producers who are often not as rigorous in meeting the standards of animal welfare and care for the natural environment."
Mrs Prentis, a minister in DEFRA, the Department for Environment, Food and Rural Affairs, voted against the amendment. She said: "The Bill... will ensure that those who produce our food are properly rewarded and that farming efficiently and improving the environment will go hand in hand in the future.
“I was elected on a very clear manifesto commitment - one that the Prime Minister has reiterated since - that in all our trade negotiations we will not compromise on our high environmental protection, animal welfare and food standards. This Government will stand firm in trade negotiations to ensure that any deals live up to the values of our farmers and consumers.”
However Farmers Weekly - the farming journal - said in an article: "(The amendment) was defeated by 328 to 277 votes - a majority of 51 - after failing to receive the support of the Conservative government, despite several previous commitments to safeguard our farming industry from cheap food imports, produced to standards that would be illegal in the UK.
"Despite priding themselves on being 'the party of the countryside', only 22 Conservatives voted to support (Neil Parish, Conservative MP for Tiverton and Honiton's) defeated amendment."
North Dorset MP Simon Hoare, who voted against his party, said food imports would be cheap 'for no other reason bar the fact that they were raised to lower standards' and raised the issue of sine 'pretty horrendous ways in which livestock is raised in a number of countries across the world'.
Farmers Weekly reported former Defra secretary Theresa Villiers is said to be drawing up plans to cut tariffs on US food imports to secure a free trade agreement with the US.
Britain will leave the EU's common agricultural policy when its leaves Europe. This fund puts £3.5 billion into UK agriculture.
You can read the Farmers' Weekly story here.