Mr Rigby, chairman of World Challenge Expeditions and a partner in the North-east Lincolnshire zone, believes the innovations that businesses are supposed to bring to disadvantaged schools may be stifled by local politicians.
That hasn't stopped him from trying to extend his interests in the zones. His firm showed an interest in 12 bids in this second round and was named in six. Four - Dudley, Sandwell, Corby and Barrow - have reached the second stage.
Mr Rigby's company provides school trips to challenging destinations and runs residential courses teaching young people self-development. He believes such skills will help raise standards in socially-deprived zone areas.
But his initial experience has been frustrating. He said: "The purpose of EAZs is for people who have been running schools to invite outsiders in to bring in new ideas and innovation. This comes with substantial amounts of money from the Department for Education and Employment and there is a strong temptation for the people who have always run schools to get their hands on it and appropriate it for the programmes they have been working on."
He said that he had not been able to achieve as much as he hoped in Grimsby because "the local politicians have a different agenda from me".
But Bill Carr, the zone's director who has been seconded from a local school, said: "World Challenge has been an extremely valuable partner and we have increased the budget for its part this year. Our priority has been to introduce information technology, which has been expensive." He denied the local authority was running the zone.
In the four second-round bids, the firm is offering extra-curricular activities, study support, residential experiences and personal development programmes.