The society has asked Burnham to look at preventing content aggregators such as Google from profiting from third-party news content, without paying the companies that spent money generating it.
It wants the Government to discourage the development of local government websites, which it claims compete with local newspapers, and is encouraging the Government to advertise jobs in regional papers.
The letter also calls on the Government to recognise that advertising in regional titles is in the public interest and asks it to remove the threat of relaxing obligations for public bodies to advertise notices in local papers.
The letter is a response to Burnham's recent call to the regional newspaper industry to provide him with a 10-point plan, demonstrating how the Government could help the sector.
Burnham's call is one of several ongoing government-led initiatives. As part of Lord Carter's interim Digital Britain report, the Office of Fair Trading is investigating local media ownership rules. Regional media firms want a relaxation of rules to encourage consolidation in the industry.
A meeting last Wednesday with Burnham was attended by representatives from the Society of Editors and regional publishers' association the Newspaper Society, including Mark Dodson, chief executive, GMG Regional Media; Nigel Pickover, editor, Evening Star (Ipswich) and president of the society, John Meehan, editor, Mail News & Median (Hull) and regional editorial director, Northcliffe North East; and Michael Pelosi, managing director, Northcliffe Media.
At the meeting Andy Burnham said to the regional media representatives: "Don’t think you are alone in the wilderness. We are now going to make a concerted effort to this."
Pickover said the Society of Editors and the Newspaper Society were pleased Burnham was concerned about the "special problems" of the regional press and claimed the society's ideas could have a direct effect on local and regional papers.
Pickover said the problems facing regional newspapers were "serious and urgent", but added that the industry was not asking for special treatment but rather for government action to help ensure there was a level playing field among media owners of all types in a rapidly changing media marketplace.