A new born baby being treated for Lassa fever has died at the Luton and Dunstable Hospital.
The infections are linked to recent travel from West Africa, where the disease, an Ebola-like virus, is endemic, according to the UK Health Security Agency (UKHSA).
NHS East of England declared a "regional major incident" after news emerged of the infections, the first cases of the disease in the UK for more than a decade.
Dr Susan Hopkins, chief medical adviser at UK Health Security Agency (UKHSA), had said the cases were linked to recent travel to West Africa, where the animal-borne disease is endemic.
Last week a UKHSA statement says: "The 'probable case' is receiving care at Bedfordshire Hospitals NHS Foundation Trust with The High Consequence Infectious Disease Network engaged with their ongoing care."
Dr Susan Hopkins, Chief Medical Advisor at UKHSA, said: "We can confirm that two cases of Lassa fever have been identified in England, and a further probable case is under investigation. The cases are within the same family and are linked to recent travel to West Africa.
"Cases of Lassa fever are rare in the UK and it does not spread easily between people. The overall risk to the public is very low. We are contacting the individuals who have had close contact with the cases prior to confirmation of their infection, to provide appropriate assessment, support and advice."
"UKHSA and the NHS have well established and robust infection control procedures for dealing with cases of imported infectious disease and these will be reinforced."
In an email to staff, seen by the BBC, Cambridge University Hospitals NHS Trust, which runs Addenbrooke's, said: "Colleagues identified through our staff contact tracing exercise have been required to undertake a precautionary isolation period of 14 days, and not have patient contact for 21 days.
"As expected, this is impacting on our staffing levels and has required the temporary closure of a substantial portion of our critical care capacity - with impact on our clinical services.
"We want to assure you all that cases of Lassa fever are rare in the UK and it does not spread easily between people. The overall risk to healthcare staff and other patients is very low."
Sources also told the BBC the neo-natal unit at the Luton and Dunstable Hospital has also been closed to new admissions.
Since 1980 there have only been eight cases of Lassa fever imported to the UK - with the last two in 2009.
Lassa fever is an acute viral haemorrhagic illness caused by Lassa virus. People usually become infected with Lassa virus through exposure to food or household items contaminated with urine or faeces of infected rats – present in a number of West African countries where the disease is endemic. The virus can also be spread through infected bodily fluids.
Most people with Lassa fever will make a full recovery, however severe illness can occur in some individuals
There was no evidence of onward transmission from any of the previous UK cases.