The company has switched its focus away from a New York listing in response to fierce political opposition in the US. Mr Rubio was one of the most vocal critics of the company, writing to the US Securities and Exchange Commission to block a New York listing unless Shein was more transparent over its operations.
Concerns centre around Shein’s Chinese supplier-base. Most Chinese cotton comes from Xinjiang, where there is alleged forced labour of Uyghurs.
Mr Rubio, a former Republican presidential candidate, said in April that there was a “high probability these companies have facilitated the importation of goods made with forced [sic] labor”.
In his letter to Mr Hunt, Mr Rubio said: “The United Kingdom has a storied tradition of abolitionism, from Wilberforce and Cowper to the Modern Slavery Act in our day.
“I trust you will treat these allegations against Shein with the utmost seriousness, investigate them fully, and take appropriate action to protect investors.”
Mr Hunt held talks with Shein executive chairman Donald Tang in January, which was seen as a bid to convince the fast fashion retailer to choose the London Stock Market.
Labour recently suggested it would also be supportive of Shein choosing London. MPs from the party have also met the retailer, saying afterwards that “raising investment, productivity and growth is one of Labour’s missions for government”.
Shein, which was founded in China but is now headquartered in Singapore, has repeatedly denied claims of forced labour in its supply chain.
The company said it has “a zero-tolerance policy for forced [sic] labor” and is “committed to providing a safe and fair work environment to all our suppliers’ employers”.
It said its success is a result of its “on-demand business model and flexible supply chain”.
Mr Rubio is among the front-runners to be picked by Donald Trump as his running mate in the upcoming US elections.
ABC News reported last week that he was one of a handful of people asked for vetting paperwork as the vice presidential candidate field narrows.