Thorp said the shoe rule was too much, saying that formal dress codes are "outdated and sexist" and should reflect society.
Her online petition has more than 150,000 signatures, which opened the door to debate in Parliament, The AP reported.
While the debate held this week is non-binding, the pressure for companies to remove the high heel rules is gaining steam. British law forbids companies from female discrimination, but Parliament's Women and Equalities Committee said that dress codes that single out women are still common.
Not only is there a discriminatory feel to the rules, doctors testified that women who wear high heels for long periods have "reduced balance, reduced ankle flexion and weaker muscle power in the calf" and could lead to disabling pain.
The petition is already influencing the workplace. Thorp’s employer Portico announced last year that it would have a gender-neutral dress code that will allow workers to wear flats if they would like to.