The UK has returned a first failed asylum seeker to Rwanda under a voluntary removals programme, it is understood.

Under the scheme, announced last month, migrants whose claims are rejected are offered up to £3,000 to move to the east African country.

It is separate to the forced returns scheme the government announced two years ago.

That scheme, which has been beset by delays, is due to begin by mid-July.

The Sun, which first reported the story, said the unnamed man was flown out of the UK on Monday on a commercial flight.

Officials would not be drawn on any details, other than to say the asylum seeker had exhausted all rights to be in the UK.

Labour said the move showed ministers were “desperate” to get a flight off to Rwanda before Thursday’s local elections in England.

The scheme announced in March is understood to be a variation of an existing voluntary returns scheme for failed asylum seekers.

The scheme will also be opened up to other people with no right to remain in the UK, and foreign criminals.

The Home Office says payments under the current scheme “can pay for” temporary accommodation in the destination country, or education costs, or the cost of setting up a business.

According to official statistics, 19,253 people with no right to remain in the UK were voluntarily removed from the UK last year.

Of these, 3,319 received a “reintegration package” or flights paid by the Home Office.

Shadow foreign secretary Yvette Cooper called news of the voluntary return a “pre-election gimmick,” adding taxpayers were “forking out £3,000 for a volunteer to board a plane”.

“The Tories are so desperate to get any flight off to Rwanda before the local elections that they have now just paid someone to go,” she added.

It comes after the Home Office confirmed Rwanda had agreed to accept an initial cohort of 5,700 asylum seekers under the separate forced returns scheme.

The scheme – which the government argues will deter future migrants from crossing the English Channel in small boats – has been dogged by legal delays.

However, it is finally set to begin in the summer, after legislation to override a Supreme Court ruling entered into force earlier this month.

The Home Office has said 2,143 asylum seekers can immediately be located for detention in the run-up to their flights, as they are reporting to the department.

It has denied losing track of the remaining 3,557, who are subject to a range of different monitoring requirements.

Downing Street insisted on Tuesday it remained confident of their whereabouts, after the figures became public as part of a policy document.

However, a government source admitted it was possible some could abscond before they were detained.