The government is facing a backlash over plans to change the law to give cabinet ministers six months’ maternity leave on full pay, allowing the attorney general, Suella Braverman, to keep her post after having her baby but excluding backbench MPs from similar rights. Labour will back the move, but it has caused some disquiet among backbench MPs angry that the maternity rights will only apply to secretaries of state, and go further than those that apply to the general public. Under existing laws, Braverman would have to resign if she wanted to take time off following the birth. MPs are entitled to take paid maternity leave but are not automatically guaranteed any cover, meaning in practice many do not take leave. Despite its backing, Labour is concerned that no provisions have been made for paternity leave or other parental rights because of the urgency of having the measures in place before Braverman gives birth at the end of the month. The TUC said it was concerned the bill would amount to a two-tier system and had broader implications for workers’ rights. A number of feminist organisations, including the Centenary Action Group and the Fawcett Society, also raised concerns about the bill and have called for the scope to be wider. It is understood that some MPs are looking at amending the bill – though so far they have been told its scope means it cannot be expanded to include backbenchers. Labour’s Stella Creasy, who campaigned for MPs to have the right to locum cover while on maternity leave, said the bill presented parental rights as a “bonus” for being promoted and not for those in the lower ranks. “In no other workplace would guaranteed paid maternity leave and cover be only the preserve of the management,” she told the Guardian. “The introduction of cover for ministers is long overdue, and this legislation reveals the lie I was told when I asked for maternity cover that MPs’ employment status made it impossible. Two years on, the situation has not changed, and other MPs who have tried to get cover have been let down. “What message does it send to the thousands of pregnant women facing redundancy and job insecurity in the pandemic or any of those considering entering public life at any level, if parliament treats maternity leave as a bonus like a company car to be given only to those at the top?” Labour sources said the government had committed to further, broader legislation before the summer recess that would address paternity or shared parental leave, adoption leave and potentially sickness leave for ministers on a cross-party basis. Rachel Reeves, shadow cabinet office minister, said it was a “small but significant step forward for women’s rights in parliament”, but said there remained gaps in the legislation. “This bill is already out of date, with no provisions for paternity, adoption or shared parental leave. Labour intends to hold the government to their word to work cross-party to introduce comprehensive legislation,” she said. Previous rules would have meant Braverman would have had to resign if she had wanted to take any leave, or had her ministerial duties split between other ministers rather than have a full-time replacement. Whips have indicated that they hope to pass the whole bill in a single day on Thursday. The Guardian understands that Labour believes the major outstanding issues with the bill cannot be resolved in time for Braverman to take her maternity leave. The party will not table any amendments from the front bench, though backbenchers may still try to amend the bill. Adding paternity and shared parental leave to the bill could potentially create a loophole where ministers and their employed partners could both take six months’ paid leave together, giving ministers greater rights than the general public. The TUC’s general secretary, Frances O’Grady, said: “All workers should have access to decent paid maternity and paternity leave – including MPs and ministers. There shouldn’t be a two-tier system that privileges some new mums.” Helen Pankhurst, who leads the Centenary Action Group, which campaigns on women’s representation and participation in politics, said it was “one rule for the cabinet and another for MPs, who still don’t have maternity rights or any formal parental leave.” Pankhurst, the great-granddaughter of Emmeline Pankhurst, said: “In February 1918, the government gave the right to vote to only some women and it took another 10 years for women to be given equal voting rights as men. We can’t wait another 10 years for parliament to be fit for the 21st century.” Felicia Willow, chief executive of the Fawcett Society, said it was now an urgent matter that MPs be given paid maternity cover, but urged the government to address maternity rights disparities across the country. “Most working mothers on low incomes are expected to survive on very low [statutory maternity pay] or maternity allowance, the payments for which will be deducted for any claims for universal credit,” she said. “The government must not only support its own, but must also help and support all women on maternity leave.”