Ms Thorp said she would have struggled to work a full day in high heels and had asked to wear the smart flat shoes she had worn to the office in Embankment.
But instead she was was told she should go and buy a pair of heels on her first day, back in December.
"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," Ms Thorp told BBC Radio London.
"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'."
Ms Thorp said she asked if a man would be expected to do the same shift in heels, and was laughed at.
She then spoke to friends about what had happened, and after posting on Facebook realised that other women had found themselves in the same position.
"I was a bit scared about speaking up about it in case there was a negative backlash," she said. "But I realised I needed to put a voice to this as it is a much bigger issue."
She has since set up a petition calling for the law to be changed so women cannot be forced to wear high heels to work. It has had more than 10,000 signatures, so the government will now have to respond.
Is this legal?
As the law stands, employers can dismiss staff who fail to live up to "reasonable" dress code demands, as long as they've been given enough time to buy the right shoes and clothes.
They can set up different codes for men and women, as long as there's an "equivalent level of smartness".
"I don't hold anything against the company necessarily because they are acting within their rights as employers to have a formal dress code, and as it stands, part of that for a woman is to wear high heels," Ms Thorp said.
"I think dress codes should reflect society and nowadays women can be smart and formal and wear flat shoes.
"Aside from the debilitating factor, it's the sexism issue. I think companies shouldn't be forcing that on their female employees."
Simon Pratt, managing director at Portico, said it was "common practice within the service sector to have appearance guidelines", which Ms Thorp had agreed to.
"These policies ensure customer-facing staff are consistently well presented and positively represent a client's brand and image."
However, he said the firm had "taken on board the comments regarding footwear and will be reviewing our guidelines".
A PwC spokesman said the company was in discussions with Portico about its policy.