The commission's response to a request by Third Sector under the Freedom of Information Act show that it opened 17 complaint cases into the RSPCA in 2015, with Oxfam, the British Red Cross and the Camphill Village Trust, a charity that manages communities for disabled people, in joint second place with seven apiece.
The animal charity was also the most complained-about charity in the year to March 2014 the last time Third Sector requested the information.
A spokesman for the RSPCA said that none of the complaints against it resulted in a statutory inquiry being launched by the commission.
"Like all organisations we occasionally make mistakes," he said. "When we do so, we hold our hands up and try to ensure we do better in the future."
The 10 charities with the highest number of complaint cases were:
RSPCA (17 complaint cases opened)
British Red Cross (7)
Camphill Village Trust (7)
Action Aid for Animals (4)
The numbers refer to the volume of complaints followed up by the commission rather than the number of actual complaints, many of which were not recorded because they were judged by the regulator to fall outside its remit.
Lucy Breakspere, complaints and freedom of information manager at the commission, said the number of complaints received about a charity did not necessarily mean the organisation had acted wrongly or contrary to its charitable purpose.
"For example, if a charity has taken a well-considered but unpopular decision, this might result in complaints but does not mean that the trustees have acted improperly," she said.
She said that the commission could not disclose which of the complaints resulted in further action or the nature of any action taken because this could cause reluctance among charities to cooperate or enter into open and frank discussions with the regulator.
Such disclosure would also prejudice the "consideration and assessment of any regulatory action the commission might be minded to take", she said.
A spokesman for the commission said it could not disclose the nature of the cases under investigation for the same reasons.
A spokeswoman for Oxfam said: "It is right that the public is able to raise concerns and have them investigated thoroughly to identify whether or not there is any wrongdoing. Oxfam works constructively with the commission and other regulators and responds positively to any findings and recommendations."
A spokeswoman for the Red Cross said: "We value each and every supporter and take every complaint we receive very seriously. The commission referred only one complaint to us in 2015, and no regulatory action was taken."
Andy Paton, director of communications at the Camphill Village Trust, said: "CVT was subject to a high-profile campaign in 2015, which included legal action. We're now in a mediation process with those involved in the campaign, looking to positively resolve the outstanding issues. In the meantime, the commission has confirmed there is no reason to take any action against the charity on any issues raised."
Joanne Lowe, vice-chairman of the Arab Horse Society, said that any complaints about the charity were not followed up by the commission and must have been unfounded. "We are unaware what some of the complaints were, but we do know they came mainly from one source," she said.
Mark Lever, chief executive of the National Autistic Society, said that out of the four complaint cases about the charity, the commission contacted it about only one. "That case was closed and no further action was taken after we’d investigated and explained the background to the commission," he said.
Sheila Smith, founder and secretary of Capricorn Animal Rescue, said the complaints against the charity had all originated from the same source.
She said a group of people ran a "long, dirty campaign" in which they tried to take over the charity. "These people have now been removed by the members, by the commission and by the police," she said, adding that the charity was moving on and recovering from the damage done by the group.
Brendan Rogers, a trustee at Knighton Community Support, said the charity received correspondence from the commission last October regarding complaints relating to the charity’s protocols and an annual general meeting held by the charity in September 2015.
"We have thoroughly investigated all the issues raised and have taken decisive action to satisfactorily address all their concerns," he said.
Kendra Pinder, chair of Action Aid for Animals, said a witch-hunt against the charity had been spearheaded by an organisation whose treatment of animals her charity had opposed. "We went through hell and back on Facebook last year," she said.
The Royal British Legion declined to comment.