Rumfitt, who left his job as Edelman’s public affairs lead last month, has brought Capco with him from the agency.
Rumfitt handled Capco's £8bn Earl's Court redevelopment plans, which sparked protest outside Edelman’s offices last year.
Explaining the name of the new agency, Corporate Reputation Consulting, Rumfitt said: "Corporate comms and public affairs are indivisible from each other, and the separation of the two is completely out of date.
"I believe reputation is the most important thing a company has, so we will exist to help companies promote, defend and nurture their corporate reputation, whether it is corporate affairs or public affairs."
Roberts joins after a six-month stint at the British Retail Consortium, where work included a campaign to get the Government to review business rates.
Before this, his career included heading up comms at Energy UK and leading PR for new projects at Network Rail.
Also joining the pair is account director Lyndsey Drea, who formerly worked for Rumfitt at Edelman.
Rumfitt said his aims were for CRC, which is based in Waterloo, to "more than double in size" by the end of the year. He added: "We’re ambitious to grow and the early signs are that the appetite for the agency is strong."