It emerged this week the former 'cabinet enforcer' has accepted a non-executive directorship with the London and Brussels PA outfit, after an approach by its chairman, former MEP Alan Donnelly.
He is believed to be the only serving MP to be paid directly by a public affairs firm.
Cunningham said he has registered the interest with the House of Commons and denied the role is a conflict of interest: 'I will not be working with clients and won't have a portfolio. My role will be to help Sovereign as a business and offer advice to its staff.'
But the move has been criticised by the Association of Professional Political Consultants and the PRCA's PA group.
Both said Sovereign could not join their ranks as hiring a sitting MP breaks their rules.
PRCA spokesman Martin Cairns said: 'It's not something that is good for lobbying. If Sovereign was a member it would go through our disciplinary procedures.'
APPC chairman Warwick Smith added: 'It's simple - you can't have a financial relationship with a serving MP.'
Donnelly added he had consulted with lawyers before appointing Cunningham.
Sovereign's work includes a reputation management brief for financial news service Bloomberg - which has an interest in the Communications Bill announced in the Queen's speech. Sovereign also advises the Formula 1 management team.
Cunningham's appointment comes after it emerged that the Labour Party's head of constitutional and legal affairs Aline Delawa works as company secretary for the Campaign Company, which advises clients on gaining selection as party candidates.