The payments, which have reached £20m, have been sped up to help families affected, Trade Secretary Patricia Hewitt said.
More than 5,000 workers at MG Rover's Longbridge plant have been made redundant, and about 4,000 already have been paid, Hewitt said.
A spokeswoman for the Transport and General Workers' Union (TGWU) said it was "excellent” that the workers were getting some money. She said the figure was in line with what had been expected.
However, the spokeswoman said that because of the speed of the redundancies, many MG Rover workers did not get their statutory 90-day notice period and, as a result, were owed money.
Hewitt said that while there were firms interested in buying MG Rover assets, that would not necessarily help save jobs.
Administrators PricewaterhouseCoopers says it has been contacted by 200 firms from around the world interested in buying the assets, divisions and brands of MG Rover.
Newspaper reports over the past couple of weeks have linked MG Rover with possible buyers from countries including China, Russia and Iran.