Morgan could not take on the role of minister for equalities as she voted against gay marriage.

Benjamin Cohen, publisher of PinkNews, said it was "unfortunate that the new minister for women opposes the rights of some women, lesbians, to have the right to marry".

Morgan also backed an unsuccessful attempt by Tory MP Nadine Dorries to tighten restrictions for women requesting an abortion, voting for an amendment that would have made it compulsory for them to have independent advice.

The reshuffle means the three women in official cabinet posts are Justine Greening, the development secretary, Theresa Villiers, the Northern Ireland secretary, and Theresa May, the home secretary. Miller's departure also means there are now no mothers in the cabinet.

Morgan will be allowed to attend cabinet, along with the peer SayeedaWarsi, who can already do so in her role as a junior foreign office minister.

Gloria De Piero, the shadow women's minister, said Cameron's decision to replace Miller with Javid meant there was now no full member of the cabinet speaking for women.

"There are now just three women running government departments out of a possible 22, demonstrating that when it comes to women, it's out of sight, out of mind for this out of touch government," she said.

A wider cabinet reshuffle is expected in the summer.