Originally the agreed fee was pound;250,000, but an increase, said to be substantial, has recently been negotiated.
The Department for Education and Employment is believed to be paying three-quarters of the fee, and the council the rest.
The consultants, appointed after an Office for Standards in Education report said that Islington was not capable of tackling its weaknesses, have drawn up a shortlist of 10 companies for the contract worth pound;15 million a year.
These include Capita, which managed the nursery voucher scheme under the Conservatives, the the not-for-profit company CfBT, and Nord Anglia, which has a contract for education services with Hackney.
Nord Anglia has been offered extra work by Hackney to ensure that its takeover of some of the east London borough's education services goes ahead.
The company had asked the council to indemnify it for redundancy costs of up to pound;195,000 for six of the 26 posts it was due to take over on July 1.
Hackney refused, but has said if the posts are made "redundant", it will transfer extra work to Nord Anglia to enable the staff to continue to be employed by the company.
The amended contract, details of which have been passed to The TES, was due to be signed this week.