The Pacific island of Samoa has been overwhelmed by more than 5,500 cases of the disease.
Seventy-nine people have died, nearly all of them are children under five.
The British medics are working alongside local teams and volunteers from around the world.
“It’s quite something when you see a ward full of people with measles, they look so sick, it’s not something we’re used to,” Dr Rachel Anderson, an A&E consultant in Edinburgh, told the BBC.
“To my knowledge, I’d never seen measles… you feel like you’ve got a bit of catching up to do.”
Rachel was on call with the UK Emergency Medical Team.
The organisation deploys NHS staff to emergencies around the world.
It sent doctors and nurses to tackle diphtheria spreading through Rohingya refugee camps in Bangladesh last year and to help with the massive Ebola outbreak in West Africa in 2014-15.
Measles led the Samoan government declared a national emergency in November.