In a report on a 10-month investigation of the British Red Cross, Macmillan Cancer Support, the NSPCC, Oxfam and GoGen, the FRSB said the charities had breached the Code of Fundraising Practice by failing to adequately monitor the agency's fundraising activities.
Macmillan and the BRC also breached industry guidelines by failing to make it clear to supporters how their contact data would be used, said the report.
The FRSB found that GoGen breached the clause in the code that prohibits vulnerable people from being exploited. It also advocated the use of pressurising techniques during training sessions and failed to make clear that the purpose of phone calls was to seek financial support.
The FRSB launched its investigation in July after allegations were made on the front page of the Daily Mail that GoGen was "exploiting loopholes" in the Telephone Preference Service. The agency ceased trading later that month, citing a "reduction in business resulting from misleading media coverage".
The FRSB found that the charities had not breached the code of practice rules on the TPS as they were at the time of the Daily Mail's report.
The regulator also dismissed the Daily Mail's allegation that GoGen fundraisers were trained to deliver a solicitation statement only at the end of a fundraising call, saying it found no evidence this was the case.
Andrew Hind, chair of the FRSB, said: "Ultimate responsibility always rests with charities for the conduct of any third-party agencies representing them. We welcome the significant actions that each charity has since undertaken."
Peter Wanless, chief executive of the NSPCC, said: "Specific fundraising actions exposed at GoGen were unacceptable and the NSPCC terminated its relationship with it. We accept it would have been good practice to keep better records of our monitoring activity and have made substantial changes to our fundraising operation."
Mark Goldring, chief executive of Oxfam, said: "I would like to apologise once again for the fact we did not spot that GoGen was falling well below the high standards both we and the public expect."
A spokeswoman for the BRC said: "We were hugely disappointed to learn last year of the behaviour of GoGen agency staff. It was completely unacceptable and not only did we suspend our work with them, but also all of our telephone fundraising while we conducted a full review of our standards and procedures."
Lynda Thomas, chief executive of Macmillan, said: "We are extremely sorry that the work undertaken by GoGen on our behalf did not meet the high standards we expect."