The BBC understands that the Hillsborough Law campaign’s legal team will be in parliament next week to meet MPs in an effort to break the deadlock and galvanise support.
Barrister Pete Weatherby KC, who is a director of the campaign group, told the BBC: “The government has now made it impossible to pass the Hillsborough Law within this parliamentary session.
“They have timed us out. Even if we resolve things soon, there isn’t time for it to progress through the House of Lords in time.”
Weatherby added: “The government has withdrawn its own proposal on how the bill applies to the security services but won’t adopt ours, or tell us what they think is wrong with it. The impasse is on their side, not with the families or campaign.”
Campaigners hope the bill will finally be passed in the autumn, and the BBC has been told that ministers were committed to carrying it over into the next parliamentary session.
A government spokesperson said: “The Hillsborough disaster will remain in our national consciousness for its tragedy and disgraceful injustice.
“New legislation will ensure the state must always act for the people it serves by preventing cover-ups and ensuring accountability in public office.
“It will apply to the intelligence services and must protect our national security.
“As we have done throughout this process, we are taking the time to get this right and ensuring we never compromise on national security.”
Asked why Mahmood had turned down a meeting with the families, a Home Office spokesperson said discussions were “ongoing” with the attorney general, bill ministers and Hillsborough Law officials and that was the “appropriate forum” for those conversations.