The football may not yet have started, but the battle of the World Cup songs is already well under way with a throng of rival tunes, anti-Fifa raps and instrumental lamentations challenging the poorly received official theme by Pitbull and Jennifer Lopez.

Veteran British band, Pop Will Eat Itself will be the next into the fray this week with the release on 7 June of a politically charged single criticising the Fifa president, Sepp Blatter, and accusing the tournament organisers of fiddling billions from Brazilian taxpayers.

The official theme, We Are One (Ole Ola) came out earlier this month with a lavishly produced video, but – despite a collaboration with popular, local axé singer Claudia Leitte – it has gone down poorly in the host nation with many people complaining of cultural stereotypes and too brief a section in Portuguese. Many online commentators in this socially networked nation said how much they preferred the 2010 tune Waka Waka by Shakira.

Rival songs include Pais do Futebol (Football Nation), ostentatious funk by MC Guime that has racked up more than 23 million page views on Youtube. Featuring the rapper Emicida and Neymar, a Brazilian national team striker, it contains a message of self-improvement as a means to escape poverty. This is a popular theme in Brazilian society, where millions are trying to move into the middle class. "Look how far we've come," sings MC Guime in the chorus.

More critical is Desculpa Neymar (Sorry Neymar) a plaintive critique by Edu Krieger that highlights some of the grievances of the anti-World Cup protests that have taken place across the country since last year. Available on YouTube and played over a montage of images of protests and stadiums, it has drawn more than 170,000 views.

"Sorry Neymar, but I won't support you this time," goes the lamentation. "We have beautiful, monumental stadiums while schools and hospitals are on the brink of ruin."

The song by Pop Will Eat Itself is harsher still. The UK band has previously made a World Cup single – the 1990 Touched by the Hand of Cicciolina, which called for the Italian porn star to hand over the trophy to the winners. Their latest offering is unusually political in its lyrics: "Sepp Blatter don't matter, Getting richer and fatter, His idle chatter batters the beautiful game.

"They've stole it, Trolls control it, Guard it like jewels from fools like us, Like you, Like me, Like we are peasants to the bourgeoisie, Gotta be joking, What are they smoking?"

Produced with Bnegão, a rapper based in Rio de Janeiro, the song Reclaim the Game: Funk Fifa is unlikely to get much airplay on TV and radio by comparison with the official theme, and the artists – who do not have a record label – have had to film their own promotional video. They expect to lose money, but said they wanted to get their message out.

They said their track was inspired by reports of Fifa corruption, World Cup overspending and the fury they felt when Fifa's president, Sepp Blatter, cut short a minute's silence for Nelson Mandela during last December's World Cup draw. Graham Crabb and Mary Byker, band members, said they wanted to make it the "protest song of the summer".

"You have to stand up for what you believe in. We are old enough and stupid enough to know our own minds and not be scared enough to open our mouths," said Byker. "We're not kicking football, we are kicking the establishment that runs football. The general consensus of most people I speak to in Brazil is 'Fuck Fifa'. Nobody likes the money spent on stadiums."

Their Brazilian collaborator Bnegão performed during the closing ceremony of the London Olympics after rising to prominence as a singer for Planet Hemp, best known for their advocacy of cannabis legalisation. In the song, he raps in Portuguese: "The game is ours, Football is ours, It's everyone's, It's the real passion of the people, It exists by itself, And it doesn't depend on Fifa."

"I wanted to voice the opinions of the many people who feel the same way I do about Fifa. I'm glad to be that voice," said Bnegão, who described himself as a guerrilla artist. "It's hard for mainstream Brazilian artists to do anything like this song because it could close many doors here. But I'm not afraid of that. I've never wanted to be a pop star or anything like that. My entire career was built on saying what I think."