The prime minister has been accused of making unrealistic demands for how the UK will operate after its EU exit.
Theresa May's demands are the "equivalent of a letter to Santa", the TUC's general secretary said at the trade union's annual conference.
Keeping the benefits of the EU's single market without playing by the rules is not possible, Frances O'Grady said.
The government has said the UK will strike an ambitious EU trade deal for when it leaves the single market.
Ms O'Grady told the conference in Brighton that staying in the EU single market, which enables tariff-free trade, is the best long-term option for UK workers.
But the transport union RMT opposed such a move, saying it would involve keeping "key anti-worker policies".
In her keynote speech, Ms O'Grady said the government had not spelt out the costs of leaving the single market.
She called for ministers to produce reports on how individual industries could be affected by no longer having the same access.
The EU has said the UK cannot control immigration of EU workers and strike trade deals with other countries while it is still a member of the single market.
As well as eliminating tariffs, quotas or taxes on trade, the single market also includes the free movement of goods, services, capital and people.
It also strives to remove so-called "non-tariff barriers" - such as different rules on packaging, safety and standards - so the same rules and regulations apply across the area.
The TUC is concerned EU rules on workers' rights could be diluted when the UK leaves, saying this would produce a "sweatshop Brexit".
However, the RMT union said workers were ill-served under the EU because of policies like rail privatisation and social dumping.
"We would be kept under the iron grip of the unelected Brussels bureaucracy with control remaining out of our hands," said RMT general secretary Mick Cash.
A government spokesman said it would "ensure that workers' rights are fully protected and maintained" after the UK leaves the EU.
"We will build on our economic success by establishing a deep and special partnership with the EU while embracing the wider world as an independent, open, trading nation," he added.