More than two million people have been granted the right to carry on living and working in the UK permanently after freedom of movement ends, figures suggest.

EU citizens and their families are asked to apply to the Home Office’s EU Settlement Scheme (EUSS) by June next year in order to carry on living and working in the UK when the transition period with the European Union ends after Brexit.

Some 2,041,200 people were granted settled status after applying to the EU Settlement Scheme, according to provisional Home Office statistics to the end of July.

A further 1,475,500 were granted pre-settled status, where they would need to reapply again after living in the country for five years to gain permanent residence.

But 4,600 applications were refused, 36,500 were withdrawn or void and 34,900 were invalid – where the Home Office decides someone is not eligible to apply or has failed to provide sufficient proof of residence.

More than 3.8 million (3,805,200) applications have been received in total so far, with some 3.5 million (3,516,700) of those concluded.

After a drop in the number of applications being submitted and processed during the peak of the coronavirus pandemic, the department said it received 92,000 in July and dealt with 133,100 during the month.

The figures prompted the Liberal Democrats to reiterate calls for EU citizens to be given an automatic right to stay in the UK and proof of this with documentation to avoid “a new Windrush-style scandal”.

The party’s home affairs spokeswoman Christine Jardine said: “For far too long, millions of EU citizens in the UK have been living under a cloud of uncertainty. Boris Johnson cannot be allowed to continue to break his promise to them.

“With so many people being refused settled status, granted only temporary ‘pre-settled status’ or still waiting for a decision, it’s clear that this Conservative Government’s scheme is anything but automatic.

“And without physical proof of their rights, EU citizens will be at the mercy of the Conservatives’ hostile environment. They must not become the victims of a new Windrush-style scandal.”

Immigration minister Kevin Foster said EU citizens were an “integral part of UK society” and 3.5 million had already secured their rights in UK law, adding: “There’s plenty of time left to apply before the June 30 2021 deadline and a wide range of support is available online, over the telephone and in person if you need it.”

The next official quarterly figures on how the scheme is progressing are due to be published towards the end of the month.