The all-party Commons Public Administration Committee will condemn the Home Secretary's decision to water down the Government's original proposals and call for him to make a much greater commitment to openness.
Although Mr Straw has already indicated his readiness to make some concessions to his critics, the report, which is due to be published on Thursday, is expected to highlight a number of areas in which the MPs still find his position unacceptable.
They are furious that the Government is determined for ministers to have the final say on whether or not they release information.
The MPs believe that the new commissioner for freedom of information should be given the power to order departments to hand over documents.
The committee, which is headed by the Labour MP Tony Wright, a long-standing advocate of greater openness, is also expected to criticise the number of areas that are exempted in the draft Bill.
Those areas include policy advice given to ministers by their officials and information about accidents or disasters.
During his evidence to the MPs, the Home Secretary indicated that he was ready to reconsider the scope of the exemptions.
But the MPs believe that there are also basic principles that need to be reassessed. They are convinced that the Home Secretary, by giving ministers and civil servants the right to veto the release of documents, has failed to subscribe to the principle of freedom of information.