The TUC said five million employees regularly work extra hours without financial reward. On average they put in the equivalent of one extra day every week.
The findings come at a sensitive time for the government, which is fighting to preserve the "opt-out" clause in the EU Working Time Directive, which allows workers to waive their right to a maximum 48-hour week.
Opponents of the opt-out clause will use the TUC research to argue that millions of staff are put under pressure to work more hours than they want.
The research suggested that the average worker who puts in unpaid overtime would receive an extra £4,500 a year if paid at their usual rate, increasing the earnings of the average full-time employee by 18%. This adds up to £23bn - more than 4% of the UK's total wage bill.
Unpaid overtime is most common among managers, where more than 1.5 million managers are working more than their contracted hours.
Ministers already face pressure from the unions, the European Commission and EU member states to change their stance over working hours.
John Cridland, deputy director general of the Confederation of British Industry, said, "Most people work extra hours because they want to, but they should have the freedom to choose."