An application system for EU nationals seeking to remain in the UK after Brexit will be "as easy to use as setting up an online account at LK Bennett", according to Amber Rudd.
The Home Secretary referred to the fashion retailer during a private business dinner earlier this month, the Financial Times reported.
LK Bennett describes itself as an "affordable luxury brand", selling shoes, clothes, handbags and accessories.
The outlet is a favourite of a number of high-profile women including Theresa May and the Duchess of Cambridge.
Ms Rudd reportedly made the comments as she told business leaders at a meeting in London that her department was taking steps to ensure the smooth registration of EU nationals using a digital system.
But campaign organisation the3million, which represents EU citizens living in the UK, accused Ms Rudd of "trivialising" the "serious" application process.
The body added: "We had to Google LK Bennett, a popular chain with the upper middle class.
"It just shows how detached the Government is from the real concerns of the average EU citizens."
Officials are preparing from scratch an online application scheme that will be open to more than three million EU citizens living in the UK later this year.
Those who have been in the country for five years by the end of 2020 will be able to apply for settled status, meaning they are free to go on living and working in the UK.
People who have arrived by December 31 2020, but do not have five years residence, will be able to apply to stay until they have reached the threshold, at which point they can seek settled status.
Applicants will have to provide an ID document and a recent photograph, as well as declare any criminal convictions.
The scheme will go live towards the end of this year and remain open until the end of June 2021.
Ministers have said the system will be quick and easy to use, taking a matter of minutes to complete.
The Home Office said: "We are developing from scratch a new digital, streamlined, user-friendly scheme for EU citizens to safeguard their right to stay in the UK after we leave the EU.
"We are working closely with EU citizens as part of its development.
"Technology will play an important role in making applications as simple and quick as possible. We will draw on existing Government data to minimise the burden on applicants to provide evidence. "