However Stevens concluded there was no evidence of illegal payments to club officials or players and said the clubs had all fully cooperated with his investigation.
The former police chief expressed serious concern over the conduct of 15 agents, including Zahavi, one of the most high-profile figures in the game, who Stevens recommends should be subject to a Fifa investigation.
Graeme Souness, former Newcastle manager, is also placed firmly in the spotlight, with the report highlighting "inconsistencies" in the evidence provided by him and Kenneth Shepherd, the son of Newcastle chairman Freddie Shepherd.
In the case of Allardyce, who was manager at Bolton during the period in question, the report identifies a possible conflict of interest arising from the fact that his son Craig Allardyce, a former agent, was involved in transfer dealings with the club.
Lord Stevens' findings will now be passed to either the English Football Association (FA) or football's world governing body Fifa, depending on where the individuals identified are registered, for possible disciplinary action.
Despite finding evidence of wrongdoing in the cases he has highlighted, Stevens said that he was satisfied transfer dealings involving English clubs were largely free of corruption.
"Many lessons have been learned and strict adherence to and enforcement of the recommendations should ensure that the game and the transfer market can proceed in an untainted and transparent manner," Stevens said.
Of the 17 transfers, four relate to Newcastle signings (Emre Belozoglu, Jean Alain Boumsong, Amady Faye, Albert Luque), four to Bolton (Ali Al-Habsi, Tal Ben Haim, Blessing Kaku, Julio Correia), three to Chelsea (Didier Drogba, Petr Cech, Michael Essien), three to Portsmouth (Collins Mbesuma, Benjani Mwaruwari, Aliou Cisse) and two to Middlesbrough (Aiyegbeni Yakubu and Fabio Rochemback).
The player and club involved in the 17th transfer were not identified.
Richard Caborn, British Sports Minister, urged the FA and Fifa to crack down on agents who had not cooperated with the inquiry.
"While it's pleasing to hear that all clubs and officials have cooperated fully with the Steven's inquiry, I am deeply concerned that some agents haven't," Caborn said.
"It's now for the FA and Fifa to pursue these agents vigorously and they will have my support every step of the way.
"The role of agents in football will always be controversial and that's why they need proper regulation at national, European and international level."
The report was severely critical of Zahavi's failure to cooperate fully with the inquiry, after having initially failed to disclose his involvement in a number of transfers, before refusing to provide bank statements requested by investigators.
"There remain questions relating to his relationship with and payments to (British agent) Barry Silkman, and Barry Silkman's failure to initially disclose his involvement in all the transactions in which he received fees," the report notes.