Called Trafalgar Strategy, the agency advises on reputation management, campaigns, public affairs and "complex communication challenges".
According to a statement announcing the launch, Trafalgar will work across the corporate affairs, public affairs, sports, arts and entertainment and charity sectors and has secured clients across these industries. However, initial clients have not been disclosed.
Also working at the new agency is Elliott Burton, former special adviser to business minister Anna Soubry, who worked with Kenningham in the Conservative press office on the 2015 general election campaign.
The consultancy is based in Covent Garden.
Kenningham departed Downing Street along with other figures in Cameron’s press team when Theresa May became Prime Minister after the EU Referendum last summer.
He has appeared across the media, including the BBC, Guardian and FT, as a commentator during the current general election campaign.