A Portuguese woman who has lived in the UK for 20 years has interrupted a live Sky News broadcast to criticise the running of the EU settlement scheme and speak of her fear of being deported after 31 October.

The woman’s impassioned plea came amid growing concerns that the government scheme, which allows EU citizens to apply for settled status in the UK, could become “another Windrush scandal”.

About 1 million EU nationals resident in the UK have applied for settled status, but at least a further 2.6 million have yet to apply, while there have been concerns over complications with the application process, such as the impossibility of accessing the EU settled status app via iPhone. EU citizens in the UK contacted the Guardian in droves last week to demand clarification of their status as no deal looms.

The Conservative MEP Daniel Hannan, who supported leave in the EU referendum, called on the home secretary to sort out the issues with the scheme, warning the government could end up with another Windrush scandal.

Daniel Hannan (@DanielJHannan) I have had constituency cases of EU nationals being denied settled status despite living here for years. This is a breach of the assurances I and other Leavers gave during the referendum. Please help sort this out @patel4witham before we end up with another Windrush scandal.

The Portuguese woman who interrupted the broadcast spoke tearfully of having no voice in Brexit despite residing in the country for the past 20 years and said the “settlement scheme is not working”.

The woman said: “I work and I gave this country my youth. I’m very grateful for what you taught me but you must make me part of all this process. I can’t just be kicked out. I build things for you, I’ve looked after your children. I’ve looked after the elderly in this country. Now you kick me out with what? With what?”

She pointed at the Houses of Parliament and said: “I am very, very hurt by what they’ve done to England because I came here and I joined the working force and I’m very proud of it, and I’m very angry at them for doing this to this country.”

She went on to say she had problems with her EU settlement scheme because her “national insurance didn’t correspond to the right thing” and said she was being forced to restart the entire process. “But the 31st of October is fast approaching. What am I going to do? How am I going to stay? What are my rights? I’m in the dark like many, many people.”

Axel Antoni, a spokesman for the3million EU citizens’ campaigning group, said: “Our view of the settlement scheme hasn’t really changed. We’ve known from the beginning there would be issues with people proving their status.

“We sent over 150 questions to the Home Office when it was originally planned and we never received any answers. What we’re seeing now is what we expected to see.”

Antoni added it was not enough to just slightly tweak the scheme. “The answer to this is not changing the process, it’s about actually honouring the referendum process of making the settled status automatic.

“The government could immediately solve the problem by securing our rights in law which was promised in the referendum campaign and Boris Johnson’s maiden speech. It would stop all these issues, including the likening to Windrush, by making the process about registration.”

A Home Office spokesperson said: “EU citizens are our friends, families and neighbours and we want them to stay.

“The EU Settlement Scheme is free and is designed to be as simple and straightforward as possible. Applicants only need to complete three key steps – prove their identity, show that that they live in the UK, and declare any criminal convictions. More than a million people have been granted status so far, and people have until at least December 2020 to apply.

“We have over 1500 Home Office staff working on the Scheme including handling calls and emails in the Settlement Resolution Centre, helping people apply.”