Its demise means new homes will have to be found for clients including Metro, Princess Cruises, and ABC1, the Disney TV channel.
It is possible some of the business could follow Justin Cernis, Barrett's erstwhile partner, who has yet to resolve his future.
Cernis, a former senior manager at Young & Rubicam and an ex-McCann Erickson new-business director, said: "I still have lots of energy and lots to prove."
Efforts are being made to find alternative jobs for the agency's 11 full-time staff and three consultants.
Barrett's appointment to lead the 22-strong creative department at BJL - for-merly Barrington Johnson Lorains - follows discussions between himself and Cernis about their agency's future, the pair having ruled out the options of a sale or a merger.
Barrett, 47, insisted the decision to fold would have been taken irrespective of his move north.
"Running a small agency is frustrating and doesn't realise the talents Justin and I believe we have," he said. "The market is very competitive, with big agencies going after the kind of accounts that used to be ours."
At BJL, the UK's largest independent agency outside of London, Barrett replaces Steve Johnson, who retired at the end of last year. Since then, its creative department has been overseen by Pete Lewtos, a former senior creative at TBWA in New York. BJL's clients include British Airways, Pilkington Glass and Eurocamp Holidays.
Barrett's career spans spells at Burkitt Weinreich, FCO, WCRS and Ogilvy & Mather. He has two Cannes gold Lions and D&AD and Campaign press and poster silvers for work on Nike, Bass, Kimberly-Clark and Prudential.