The government is extending its live trial of post-Brexit registration for EU citizens to 250,000 people across the country in an attempt to smooth out wrinkles in its settled status scheme.

It will test the scheme with vulnerable individuals for the first time to address concerns about the capacity of the elderly and children looked after by local authorities to register in the largely online process.

The extension follows the launch of a pilot scheme in the north-west of England involving 12 NHS trusts and three universities in Liverpool.

It will run from 1 November until 21 December with participating organisations focusing on EU citizens working in the health and education sectors.

Unveiling the new scheme, the immigration minister, Caroline Nokes, said: “EU citizens make a huge contribution to our economy and we want them to stay.”

The Home Office will publish the findings from the first phase later this month but revealed that 650 EU citizens had applied. Registrations are expected to reach 1,000 by the end of the first test on 17 October.

“Overall, the technology performed well, with some minor improvements identified to improve the overall customer experience,” Nokes said.

An estimated 3.5 million to 3.8 million EU citizens in the UK will be required to apply for settled status post-Brexit.

Updating the government on the first pilot, the Home Office said the process took an average of 15 to 20 minutes to complete and nobody was refused their application for settled or pre-settled status, which applies to those who have been in the country for less than five years.

But it said there were improvements to be made to the automatic data matching made against HMRC records and some of the language used in the application process.

Campaigners such as the3million organisation and recruits in Liverpool have said the first phase should have gone well as all the recruits were highly educated and computer-literate.

The second phase will be critical in establishing how well the scheme works for the more vulnerable, with seven charities involved in the scheme.

From 1 November the scheme extension will include three NHS trusts in Manchester in addition to the 13 participating in the north-west.

From 15 November, applications will be taken on behalf of children in care in five local authorities in Kent, Lincolnshire, Sheffield and the London boroughs of Waltham Forest and Haringey.

Those eligible to apply include people receiving support from the Eastern European Resource Centre and Rights of Women and The Roma Support Group charities in London.

From 29 November EU citizens working in any NHS trust in England can apply along with 16 other health institutes, including Public Health England and the Care Quality Commission.

Those in health boards in Wales, Scotland and in health and social care trusts in Northern Ireland can also apply during this phase as can any person employed in one of the 11 medical councils across the country.