Video report by ITV News National Editor Allegra Stratton
The Home Secretary Amber Rudd has said she doesn't believe EU citizens currently living in the UK will have their right to stay withdrawn, but stressed the rights of Britons living on the continent will have to be guaranteed before this can be confirmed.
Ms Rudd told ITV News the government "would like" to assure EU citizens that they will not have to leave following Britain's withdrawal from the European Union, but said "for now it's a discussion".
The home secretary's comments come after the Government was put under pressure from the head of the NHS to assure its foreign staff that their jobs are safe post Brexit.
Mr Stevens, chief executive of NHS England, called on Theresa May to institute "bold and broad reforms" that include protecting the rights of Europeans working in hospitals and surgeries across the country.
Earlier this month Theresa May was criticised for failing to confirm whether EU nationals living in the UK will be able to stay post Brexit, telling Peston on Sunday that it would be subject to "negotiations".
When asked by ITV News' National Editor Allegra Stratton to respond to Mr Stevens' plea to reassure EU workers in the NHS of their right to stay, Ms Rudd said:
Meanwhile it emerged on Tuesday that a refugee family is living in a cottage in the grounds of Lambeth Palace, the historic residence of the Archbishop of Canterbury.
The revelation came as the Government unveiled a new sponsorship scheme that will see churches, charities, faith groups and businesses provide housing and support for those brought to the UK from Syria and other countries under resettlement programmes.
Lambeth Palace is the first sponsor approved to receive a refugee family under the scheme, which has been 10 months in the making.
The Archbishop of Canterbury Justin Welby said: "It's transformative... because it picks up on the ground surge across the country at the grass roots of sympathy and welcome of those who've been caught up in war.
"I would encourage people who have suitable accommodation who feel that they can support this to have a look and see what they can do.
"We're very good at this as a country. Historically we've done it for centuries."