Johnson revealed he met three Chelsea directors on Wednesday and they apologised for the abuse.
It recently emerged Chelsea, the current Premier League leaders, paid Johnson 50,000 pounds ($63,850, 59,230 euros) in 2015 not to go public with his allegations against Heath, who died in the 1980s.
Chelsea waived the confidentiality clause in the agreement in order to publicly apologise to Johnson, but he said the money was "not enough for the pain and suffering I've had".
He told BBC television: "It took away my childhood - I can never get that back."
Johnson revealed he met three Chelsea directors on Wednesday and they apologised for the abuse to which he was subjected during his time at the club.
Asked if he felt he deserved more from Chelsea, he replied: "Yes. It would help me build a better life. I was pushed into a corner and told I had to sign it to get the money."
Johnson is one of several former footballers to have spoken out about being abused by youth coaches during their formative years as players in a scandal that has rocked British sport.
London's Metropolitan Police said it had opened a formal investigation into non-recent allegations involving clubs in the capital. It did not say which clubs were being probed.
Detective Chief Superintendent Ivan Balhatchet said all allegations would be handled "sensitively" and "very seriously".
Twenty-one British police forces are investigating claims of sexual abuse in youth football, with hundreds of people reporting abuse.
England's Football Association has also opened an investigation.
Later Thursday news website 'The Independent' obtained details of an FA-backed investigation into child protection measures in what was intended to be a four-year project in 2001 but prematurely terminated in 2003.
The report from the FA's "Child Protection in Football Research Project 2002-06" written in 2004 said researchers were treated with suspicion by officials at football clubs, sometimes simply because they had not played the game.
"They (the researchers) were met by some traditionally robust masculine attitudes and failure to accept the relevance of CP (Child Protection) to that level of the game," read the report.
"Gaining credibility and establishing (trust from clubs) were considerable challenges, especially where researchers were unable to present credentials as current or former football players."
A problem that was highlighted -- the researchers managed to hold 482 interviews with 189 young players aged 12-17, parents and guardians, referees, managers, coaches and welfare officers -- was the inability to keep track of suspected paedophiles inside sport.
"Someone about whom there were suspicions or allegations could not be tracked from one sport to another," observed the head of the research Professor Celia Brackenridge in one interim report.
"The Criminal Records Bureau (CRB) struggled to adapt to such concern and, at the time of (our research) was not seen as a solution."
Premier League champions Leicester City and Aston Villa have also been drawn into the affair after claims about Ted Langford, who worked as a scout for both clubs.
Langford, who has since died, was jailed in 2007 for sexually abusing four young players in the 1970s and 1980s.
A Leicester spokesman said: "We take the current matter very seriously.
"At present, however, we have no indication of any allegations made against or in relation to Leicester City Football Club. We will, of course, investigate fully in the event any further information comes to light."
A spokesman from Villa said: "The club co-operated fully with the authorities during the investigation at that time (2007)."