Border staff do not feel adequately prepared to deal with the possibility of people with Ebola coming to the UK and need more information about the threat, a union leader said.
Foreign Secretary Philip Hammond sought to reassure the public over fears that the disease could come to Britain yesterday, saying it was "most unlikely" it could spread within the UK.
He did, however, describe the outbreak as a "very serious threat", and health experts have met to discuss the possibility of people contracting the virus in West Africa and falling sick here.
Public Health England has warned health officials to be on the lookout for any unexplained illness in people returning from the affected countries.
But Immigration Service Union general secretary Lucy Moreton said the union's members were very concerned and were not confident over what to do if they suspected someone of being sick.
She told BBC Radio 4's The World Tonight programme: "They serve on the front line; they are the first point of contact usually for people coming off an aircraft and the concern is what do they do if they're confronted with someone that doesn't appear well who appears at the border.
"There is no health facility at the border, there is no containment facility and until extremely recently there has been no guidance issued to staff at all as to what they should do."
Ms Moreton said members had been contacting the union for guidance on what to do and how to protect themselves, but that it had no answers for them.
Fears are rising after an epidemic of the deadly virus swept West Africa, killing more than 670 people. Ebola has no vaccine and there is no cure.
A British doctor volunteering with victims of the disease in Sierra Leone called for more help for agencies such as Medecins Sans Frontieres working in the region.
Benjamin Black, an obstetrician from Manchester who worked in hospitals in London, has been working 24-hour shifts in a clinic in the southern city of Bo, and says doctors have been struggling to cope with the pressure.
In an interview with Metro he described how he tried to save pregnant women struck with the disease, performing an emergency hysterectomy on one sufferer and helping a pregnant woman who had suffered severe bleeding and fever after preparing bodies of Ebola victims for a funeral.
Mr Black, 32, told the newspaper: "I couldn't believe this was my first shift, on my first mission. As I operated, I kept thinking I was going to drown in the pressure."
He said it was a "major concern" what might happen around the world, adding: "The main challenge here, though, is that the health authorities just don't have the infrastructure to cope. They're overwhelmed."
There have been concerns that the disease could move to the UK after it emerged two people have been assessed for the virus in Britain.
A man was given the all-clear following tests in Birmingham after he travelled from Benin in Nigeria via Paris to the Midlands, while doctors ruled out the need for an Ebola test in a second male in west London.
The Government's emergencies committee Cobra met to discuss the situation yesterday, after which Hammond said the "logical" approach was to tackle the disease at source in West Africa.
He said that the "frankly different" standards of infection control in the UK meant it was unlikely it could spread here, and that the disease appeared to be contained within the worst outbreak areas.
Health Secretary Jeremy Hunt also said that Britain had expertise in the NHS and extensive experience dealing with dangerous diseases through the work of hospitals such as the London School of Hygiene and Tropical Medicine.
The outbreak has centred on Sierra Leone, Liberia and Guinea. There has also been particular concern after densely populated Nigeria reported what is thought to be its first death from the disease on Friday.
Liberia's president ordered the nation's schools to shut down and civil servants to stay at home, while America's Peace Corps said it was evacuating 340 volunteers from the three countries.
Health workers tackling the outbreak in the region have been especially vulnerable to contracting the disease, with one doctor treating patients in Sierra Leone dying after becoming infected.
Two American health workers - a doctor and a missionary - are also in hospital in neighbouring Liberia after contracting the disease.