May has expressed a desire to grant residency protections to EU citizens currently in the UK, but cautioned this remains tied to the willingness of EU member-states to offer the same guarantees to British citizens.
But speaking at the TUC annual congress in Brighton today, O'Grady slammed the failure to offer guarantees to EU citizens.
"They are our friends, our neighbours, our workmates. It is plain immoral and inhuman to keep them in limbo. The public agrees: guarantee their right to stay," she said.
The TUC boss also demanded a role for unions in upcoming Brexit talks, warning against what she called "cosy chats" with the City and the Confederation of British Industry, and endorsing London mayor Sadiq Khan's own claims for a seat.
"We need a cross-party negotiating team, including the nations, London and the North," she said, adding: "As the voice of working people, trade unions must be at the table too."
And O'Grady also promised that unions would continue to fight against poor treatment of workers, offering employers “no hiding place”.
"To any greedy business that treats its workers like animals - We will shine a light on you," she said.
"Run a big brand with a dirty little secret? A warehouse of people paid less than the minimum wage? A fleet of couriers who are slaves to an app? Let me put you on notice."
O'Grady added: "We might organise on WhatsApp or Facebook. We might use the courts. Persuade customers. Win over shareholders. As well as recruiting workers. But there will be no hiding place."