He said: “It seems to me the Government’s reluctance to release these studies is born not of its ability to damage our negotiating position but what’s politically expedient.”
They threatened that if Mr Davis failed to release the studies within two weeks they would begin judicial review proceedings before the High Court.
Downing Street believes that publishing the documents could harm its negotiating position in talks with the EU27.
More than 120 MPs have also signed an open letter demanding that Mr Davis publish the findings, accusing the Government of keeping “not only parliament but the public in the dark”.
Mr Maugham was previously involved in the successful Article 50 case brought by Gina Miller, which challenged Theresa May’s ability to unilaterally trigger Brexit, forcing a parliamentary vote on starting the withdrawal process.
Dr Scott Cato has already unsuccessfully attempted to force the Government to release the documents through freedom of information requests.