The calls from Birmingham MPs Jess Phillips and Steve McCabe came ahead of a scheduled meeting between representatives of the families and the Home Secretary Amber Rudd in London on Monday.
The families have already appealed to the Government to make money available to fund their legal bid for answers.
Relatives of nine of the 21 people killed in the double IRA blasts in 1974 were due to meet with Ms Rudd.
A pre-inquest review into the bombings is due to be held in October but a full inquest is not expected to get under way until next year.
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Concerns have been expressed that the families of victims would be unable to meet the legal costs needed to effectively take part in proceedings.