Nicola Thorpe, 27, who has also been an actress in Doctor Who, says she was dismissed without pay and told to leave the building after arriving for her first day as a receptionist at PricewaterhouseCoopers in Embankment.
The outsourcing company Portico, which arranged her work, says its staff working at PwC have to wear shoes with a "2in to 4in heel", the BBC reported.
Thorp refused, and complained that male colleagues were not also asked to wear heels. She said she was "laughed at" after her question.
The Daily Mail reports that she was also told by Portico that she had to wear make-up in one of a selection of "acceptable shades".
She asked if she could continue wearing the smart flat shoes she had on, but she was told she should buy a pair of heels. She was then asked to leave, she told BBC Radio London.
"I said 'if you can give me a reason as to why wearing flats would impair me to do my job today, then fair enough', but they couldn't."
"I was expected to do a nine-hour shift on my feet escorting clients to meeting rooms. I said 'I just won't be able to do that in heels'."
She has now set up a petition calling for the law to be changed so employers cannot women to wear high heels to work. It has 14,000 signatures so far, meaning the Government will have to respond.
The petition reads: "It's still legal in the UK for a company to require female members of staff to wear high heels at work against their will.
"Dress code laws should be changed so that women have the option to wear flat formal shoes at work, if they wish. Current formal work dress codes are out-dated and sexist."
Sam Smethers, the Chief Executive of the Fawcett Society commented: "It is completely unacceptable in 2016 for high heels to be an essential requirement for a woman to do her job. What matters is what enables people to do a good job and what drives productivity. It is not 4 inch heels.”
Thorp has also worked as an actress and appeared in several episodes of the BBC's Doctor Who as the mother of the character Clara Oswald.