The program "Undercover - Football's Dirty Secrets" also made specific allegations involving the dealings of Portsmouth manager Harry Redknapp and Chelsea's director of youth football Frank Arnesen, as well as two agents, one of them Allardyce's son Craig.
All of those named in the program have denied any illegal dealings.
The program's accusations come before an English FA inquiry delivers its findings on October 2 into illegal payments to managers by agents as part of transfers, a system known as "bungs".
The BBC secretly recorded a number of agents accusing Allardyce of being corrupt.
France based agent Teni Yerima said Allardyce had taken money from him, while another Peter Harrison, claimed money was offered to his son on three occasions as part of various deals despite him being contractually barred from working with Bolton.
The former agent claimed his father knew of the payments although following the program’s broadcast he claimed he was overstating his importance in order to attract opportunities.
Former West Ham manager Harry Redknapp was filmed having a conversation with Harrison about Blackburn Rovers defender Andy Todd at the Portsmouth training ground.
The 59 year old denied that the conversation amounted to an illegal approach, refered to as "tapping up".
English glamour clubs Chelsea and Liverpool were both filmed having secret meetings regarding Middlesbrough's 15 year old England youth player Nathan Porritt despite Harrison saying that Boro did not know their player was being shopped around.
Chelsea's Arnesen said he could offer the teenager $282,100 a season if he left Teeside.
Both clubs denied the meetings broke any FA rules.
A former agent Steven Noel-Hill said, "The game is corrupt... Bungs were the lubricant of the deals, so in my case 8 out of 10 that means that I would say, if that goes across the industry as a whole, 80 percent of all deals have bungs attached to them…"
Former Arsenal manager George Graham remains the only high profile casualty in the English game after he was banned from the game for a year in 1995 after accepting $800,000 from the Norwegian agent Rune Hauge in connection with the transfers of John Jensen and Pal Lydersen.