British trade unions are this week expected to lend their support to a growing campaign opposed to a new international trade deal which critics claim threatens to make the privatisation of the health service irreversible.

Three of the UK's biggest unions have tabled motions at the Trade Union Congress in Liverpool outlining their opposition to the transatlantic trade and investment partnership (TTIP), a huge trade deal being negotiated behind closed doors at the European commission between EU bureaucrats and delegates from the US.

Critics say the TTIP threatens to make the outsourcing of health services in Britain permanent by allowing US multinationals, or any firm with American investors, to sue any future UK government if it attempts to take privatised health services back into public ownership, jeopardising their profits. Critics say it will also water down environmental standards and banking regulations.

Len McCluskey, general secretary of Unite, one of the unions that have tabled motions, called on David Cameron to use his veto to ensure the NHS is not included in the deal.

"It is time he put the people's concerns above the interests of a handful of US companies and Wall Street investors which want to profit from our NHS. The movement against including our NHS in this trade deal is growing and the Tories simply cannot afford to ignore it."

Efforts by the trade union movement to raise awareness of the potential consequences of the trade deal have gathered pace across Europe in recent weeks, with a coalition of environmentalists, trade unions and leftwing parties voicing their opposition.

Last week almost 10,000 people took part in more than 600 events in the UK organised by campaign group 38 degrees to leaflet and talk to people about the potential consequences of the deal. And 170,000 people have signed a petition calling on the UK to either fix or scrap TTIP.

McCluskey said: "The government and bureaucrats from Brussels thought that they could tie this deal up behind closed doors without any fuss, but ordinary people who care about the NHS recognise this danger and are making their opposition clear."

Last week the government moved to rebut accusations that the deal was being driven by the interests of big transnational companies which variously want to deregulate markets, make NHS privatisation irreversible, and water down regulations on food standards and banking.

Trade minister Lord Livingston argued that the TTIP could add as much as £10bn to the UK economy a year. He said consumers stood to gain from more choice and cheaper goods, workers would benefit from higher wages as manufacturing makes gains and small companies would be able to break into export markets.

He added that the deal, which seeks to cut remaining trade tariffs and simplify regulatory rules, will not change anything for the NHS. "The NHS and how it chooses to operate will not be impacted by TTIP."

But Andy Burnham, the shadow health secretary, said the NHS must be exempted from a deal which he said threatened the fabric of a publicly run, free-at-the-point-of-use NHS.

Burnham said: "In the EU-US trade treaty, we want designation for healthcare so that we can exempt it from contract law, from competition law. The market is not the answer to 21st century healthcare. The demands of 21st century care require integration; markets deliver fragmentation."