The Labour Leader asked Theresa May to rule out any deal that would give US healthcare firms a toehold in the NHS.
The SNP also raised concerns that such a deal will lead to the UK supermarkets being stocked with meat produced in unhygienic ways currently banned across the European Union.
The critics said the price of freer transatlantic trade will include the sale of chickens washed with chemicals.
As worries raised at Westminster over a close relationship with the US, a Tory MP demanded a guarantee the UK will not “facilitate torture”.
The former Labour leader, Ed Miliband also urged the PM to take along British scientists who could convince Trump that climate change is “not a hoax invented by the Chinese”.
May responded that her government was “very clear we don’t sanction torture” and made clear she hoped the US president will not walk away from the Paris agreement to cut carbon emissions.
But, the PM declined to discuss details of the trade, instead, saying they were to “increase prosperity and bring growth”.
Corbyn warned May of “a blank cheque to President Trump”, telling MPs: “Many have concerns that, in your forthcoming meeting with President Trump, you will be prepared to offer up, for sacrifice, the opportunity of American companies to come in and take over parts of our NHS or our public services.”
“Will you assure the House that, in any trade deal, none of those things will be offered up as a bargaining chip?” Corbyn asked.
The SNP leader at Westminster, Angus Robertson also added: “They want to export genetically modified organisms, beef raised with growth hormones and chicken meat washed with chlorinated water.”
“Will the Prime Minister tell President Trump that she is not prepared to lower our food and safety standards?” he asked.
The PM replied to Corbyn, saying that her early meeting was evidence of the bond between the two countries, “a special relationship on which he and I intend to build”.
She also responded to Robertson: “It is very simple – we want to achieve an arrangement that ensures the interests of the United Kingdom are there and are put first.”
“I can ensure the right honourable gentleman that, in doing that, we will put UK interests and UK values first,” she added.
According to Nick Clegg, the former US Vice President Joe Biden told him that the US would not agree to “anything that the chicken farmers of Delaware don’t like”.
While those farmers use chemical washes to make up for inadequate hygiene at farms and abattoirs, the EU uses a so-called “farm to fork” approach, requiring steps all along the production chain to ensure the food sold is safe.