Cobbett is to take up a new role at outsourcing services company Serco.
She will be a comms manager in Serco's 'welfare to work' division, which aims to bring long-term unemployed people into sustainable employment.
Cobbett said: 'It's a very difficult time for the COI and government comms in general. I am proud to have worked with some of the brightest and most creative minds in the industry, but the time is right to move on.
'I'm very much looking forward to the new challenges facing me at Serco and working with some equally innovative and talented people.'
The news comes as the COI awaits the news of who will be made redundant in the forthcoming sweep of cuts that will see staff numbers reduced by 40 per cent, with the loss of 287 positions.
The redundancy consultation, which is ongoing, is expected to be concluded by 1 November.
In August, the Cabinet Office announced that Government spending on advertising and marketing was down an estimated 52 per cent in June compared with the same period in 2009.