The last governors' meeting rejected a code based on shirt, tie and jacket for men and dress or skirt and blouse for women because it was felt inappropriate. The code was based on existing guidelines in the school's local authority, Westminster.
Headteacher Phil Barnard has now been asked to draft another code, which will be considered at the next governors' meeting in September.
Anthony Jones, the school's National Union of Teachers' representative, has written to Mr Straw outlining the union's objections to a staff dress code. "There can be no justification," he wrote, "for the imposition of a dress code without the consent of the staff."
Doug McAvoy, general secretary of the NUT, said that teachers should dress in a way that enabled them to discharge their responsibilities most effectively.
Glenys Roberts, a City of Westminster-appointed governor, supported a code because she thought appropriate dress was important.
"One is only asking the staff to set an example which will stand students in good stead in the grown-up world. It's as simple as that," she said.
If the governors approve a staff dress code, Ms Roberts hoped rules for students' dress could follow.
Politicians' interest in teachers' wardrobes has been increasing recently. In March 1995, the then education secretary Gillian Shephard said there was no room for flares, flowery smocks and hippy headbands, and last November praised the smartness of the staff of Earlham school in Norwich.
At around the same time, Conservative backbencher David Shaw tried to amend an education Bill to insert a requirement on smart dress for teachers, with backing from David Blunkett, then opposition education spokesman. Trainee teachers must now demonstrate that they can dress smartly.