Although fees for the business will depend on the amount of work needed in the coming weeks, it is understood a budget of several hundred thousand pounds has been made available.
The appointment comes just two weeks after the League hired City firm Holborn PR to handle the financial PR aspects of its cash demands.
ITV Digital was put into administration two weeks ago after joint owners Granada and Carlton Communications pulled the plug.
The terrestrial digital broadcaster declared itself unable to pay the remaining £178m it owed the League for broadcasting rights to lower league matches.
GPC managing director Kevin Bell will lead the agency's four-strong account team, reporting to Burns. The agency will work closely with three other sets of advisers. Law firms Hammond Suddards Edge and Lawrence Graham are spearheading the legal end of the campaign, while Holborn - whose MD David Bick referred Burns to Bell - is handling financial PR. An unnamed bank is to be hired to advise on corporate finance issues as they arise.
The day-to-day work on the GPC account will be handled by two of the firm's most recent hires. They are Andrew Lappin, a former special adviser to the then Cabinet Office minister Mo Mowlam, and Sheila Gunn, who was press secretary to former prime minister John Major.
Burns told PRWeek: 'We've hired lobbyists and a financial PR firm because we are determined to get the money we are owed. In the same way our case is being made in the media, we need it made to the political establishment - to get them to put pressure on Carlton and Granada to pay up.'