In her letter to George Osborne, Theresa May, home secretary and minister for women and equalities, said: "I fully share the objective of spending cuts. Equally it is important fairness is at the heart of these decisions so all those most in need are protected.
"In this connection there are real risks women, ethnic minorities, disabled people and older people will be disproportionately affected.
"Women, for instance, make up a high number of public workers, and all four groups use public services more. The majority of those in receipt of tax credits and welfare payments are also from these groups."
Commenting on the publication of the letter, Anna Bird, head of policy and campaigns at the Fawcett Society, said: "The Fawcett Society last week filed papers with the High Court seeking a judicial review of the Government's recent budget.
"Under equality laws, we believe the Government should have assessed whether its budget proposals would increase or reduce inequality between women and men. Despite repeated requests, the Treasury has not provided any evidence that any such an assessment took place.
"This letter clearly demonstrates the home secretary had made the chancellor – and the prime minister and deputy prime minister – aware that the Government is legally required to assess the impact of spending cuts on different groups.
"It also shows that, before the Budget was even published, there was recognition at the most senior levels of government that it risked widening inequality. The minister for equalities goes so far as to single out specific groups that look set to be hardest hit: women, ethnic minorities, disabled and older people."