FIFA president Sepp Blatter's personal position has also been called into question for his handling of the case after an ethics investigation asked whether he knew or should have known about the millions of pounds of bribes paid to his predecessor Joao Havelange and two other South American FIFA members.
FIFA granted ISL exclusive rights to market World Cup tournaments and sell television broadcast rights. A report published on Tuesday revealed Havelange has resigned as FIFA's honorary president in the wake of the findings.
Labour's shadow sports minister Clive Efford called for a completely independent inquiry into the scandal.
Efford said: "FIFA will always remain under suspicion of corruption at the very top of the organisation unless there is an entirely independent investigation into the payments relating to the ISL contract.
"It is extremely disappointing to see these people lining their pockets when volunteers that run grassroots clubs are desperate for funds. The culprits must be identified and hounded out of our game."
Damian Collins, a Conservative MP who sits on the culture, media and sport select committee and who has led a campaign for FIFA reform, insists Blatter should also resign.
Collins told the Press Association: "Sepp Blatter should himself resign for his failure to expose the wrongdoing sooner, and to take action earlier against those who had done wrong.
"The impression created by this report is one of an attempted cover-up by FIFA of this massive corruption scandal motivated by the desire to protect some of its leading officials."
The long-awaited report by FIFA's ethics committee named Havelange and two former FIFA members Ricardo Teixeira and Nicolas Leoz as receiving bribes. All three have since resigned from FIFA. The report by FIFA Adjudicatory Chamber chairman Hans-Joachim Eckert does question Blatter's role in the scandal, however.