Edward Smethurst said “calls and emails are coming in all the time” from players who say they had been forced to sign non-disclosure agreements with clubs in return for compensation.
The Offside Trust, an independent organisation set up by former footballers who suffered abuse, has also received allegations against people who still work in the “senior echelons” of the sport, the lawyer said.
The claims come after Chelsea FC apologised to former player Gary Johnson for the abuse he suffered as a trainee in the 1970s, having waived the confidentiality clause in a £50,000 agreement they made with him last year.
Speaking at the launch of The Offside Trust in Manchester, Mr Smethurst said: “Certainly, the allegations have been made by victims that confidentiality clauses have been used in relation to other clubs, but I’m not in a position to independently verify this.
“It’s unfolding as we speak. It’s a number. It’s several (but) less than five.”
The award-winning lawyer, who also chairs the Madeleine McCann Fund, said it was important that clubs “should not hush these things up and tie victims up in confidentiality”.
“We think there’s a wider perspective here and that’s the protection of victims and preventing these things from reoccurring. It’s often the case that when these things go public, other victims come forward.”
Mr Smethurst and his firm Prosperity Law LLP are advising The Offside Trust, which was set up by former Crewe Alexandra players Andy Woodward and Steve Walters, and Chris Unsworth, an ex-Manchester City youth player.
Woodward, whose interview with The Guardian nearly three weeks ago started a wave of allegations that has swept the entire game, said he and his partners are “fighting for justice” and trying to support fellow victims.
Mr Smethurst described the weeks since Woodward’s interview as a “whirlwind” and said fresh claims of historical sexual abuse at clubs are being made “all of the time”. He said the same names are being repeated.
“There are specific allegations against specific individuals, many of whom have been rumoured to be involved for a long time - some of whom still work in the senior echelons of football, and it’s extremely worrying,” Mr Smethurst said.
“There are certain names who are coming in who do come up repeatedly.”
The Offside Trust is asking for donations from the Football Association, professional leagues, the players’ union and all commercial organisations that profit from the game, as well as any private individuals who want to back the cause.
The latest police information is that new lines of inquiry are being followed at 55 clubs around the country, with Monday seeing fresh allegations about clubs and an official in Scotland.
Last week, the FA asked Kate Gallafent QC to lead a review of its response to historical allegations of sexual abuse, while Crewe have launched an independent investigation into alleged wrongdoing in their youth set-up.