Europe has a complex system for handling musicians' royalties
A video message on behalf of 38,000 UK musicians has been sent to Gordon Brown urging him to back an extension of their copyright protection.
The musicians, many of whom have worked with major artists, say they risk losing their income under current laws.
Performers' copyright runs out after 50 years but for composers and authors it extends for 70 years after their death.
The European Commission is backing an extension to 95 years from release, but the UK government is not supportive.
The video message sent to the prime minister features 29 musicians who have recorded on tracks made by artists including Frank Sinatra, The Beatles, The Rolling Stones, Madonna and Robbie Williams.
Under current copyright laws, royalties will soon dry up for session musicians who played on classic tracks released in the 1960s, campaigners say.
The musicians have been waging an ongoing campaign for support from the government, but say their message to Mr Brown comes at a critical stage because the draft European Copyright Term Directive is currently under debate.
It would extend the copyright term in sound recordings, for both the performers and the producers, from 50 to 95 years from release.
The campaigners, who are backed by the PPL, which licenses sound recordings and music videos for use in broadcast and public performance, say there is widespread, cross-party support for the changes, but so far not from the government.
The musicians argue that they receive scant reward for their role in a valuable export industry and deserve gratitude from the government.
"British session musicians are the finest in the world, the absolute finest," said Derek Wadsworth who has worked on tracks with a wide array of artists including The Beatles, The Rolling Stones and Tom Jones.
"The amount of revenue that's been brought into this country by these people is quite staggering. Now we require the government to help us out a little bit and show perhaps a bit of gratitude."
He added: "Instead they choose to kick us in the face and ignore our campaign to extend the copyright for these people and their estate."
Phil Pickett, a musician who played with '80s band Culture Club, said the amount of money a copyright change would provide musicians was small but important.
"Ninety per cent of musicians earn less than £15,000 a year. These royalties are very small but they add up over the years," he said.
But the Open Rights Group, a lobbying organisation which specialises in digital rights issues, says performers are "misguided" if they believe a copyright term extension will significantly increase their incomes.
"The European Commission's own figures demonstrate that term extension is likely to benefit ordinary performers as little as 50 cents (33p) a year," says executive director Becky Hogge.
"If Europe passes the directive to extend the term, the vast majority of financial gains - which will come direct from consumers' pockets - will go to the world's four major record labels and a handful of very famous performers."
It added that the EC had indicated artists just starting out would lose income as royalties from radio airplay will have to be shared with the estates of deceased performing artists.
A spokesperson for the Department for Innovation, Universities & Skills said: "We are sympathetic to the European Commission's goal of improving the situation for performers but we don't believe that the current proposal achieves this aim.
"The UK believes the proposal is too complex and most of the benefits will go to the record companies rather than the performers.
"The UK is still considering the detail of this proposal and it will consider future alternatives that come forward."
Shadow Minister for Innovation, Universities and Skills, Adam Afriyie, said: "Britain's artists expect a robust and even-handed set of legal protections, which is why Conservatives called for an extension to the copyright term for sound recordings more than a year ago.
"We would make that case at an international level because we want to create a level playing field for all Britain's talent.
"The prime minister must now listen carefully to our arguments and take immediate action or else he will appear seriously out of touch with the concerns of British musicians."