Mr Brown said the policy would double the existing indemnity and was necessary to protect the council if, as the Government proposes, it is given extended powers to set appraisal standards, rule on teacher competence and dismiss teachers.
The increased scope could lead to conflict with aggrieved teachers, some members feel.
This possibility came a step closer on Monday when the powers of the Parliamentary Ombudsman were extended to cover another 158 public bodies, including the GTC.
This will allow teachers to complain to the ombudsman who has wide powers to pursue complaints alleging injustice based on maladministration. The ombudsman can also investigate complaints about refusals to provide access to official information.
The decision to extend the ombudsman's jurisdiction follows the White Paper last June on Quangos - Opening the Doors, intended to provide the public with more means of redress.
The GTC's finance and general purposes committee will consider whether to recommend an increase in insurance cover at its next meeting on May 5.
This will be the latest in a series of spending decisions for the council, which could force it to put up its registration fee for teachers within the next four years. The annual fee was doubled to pound;20 last April, although that was the first rise since 1991.
Officials reported last week that the council had revised its financial estimates after providing disabled access, establishing new posts, buying computer hardware and software, introducing a new accounts package and achieving year 2000 compliance.