The forecast comes despite figures from the Public Health Laboratory showing levels of the disease returning to normal across the capital.
In May there were 16 new cases of measles, compared to 95 between January and May.
But doctors say the danger still exists and there are concerns about the low numbers of children being given the controversial MMR vaccine.
'Occurs in cycles'
More than 70% of children in London have been given the MMR jab with the recommended coverage levels being 90%.
Dr Vaz Novelli, of Great Ormond Street Hospital in London, said he believed there would be an outbreak sometime in the next couple of years.
"We know that measles occurs in cycles of two to three years and it may not happen tomorrow or next month but it will happen and there will be an epidemic," he said.
In February, more than 50 children were confirmed or suspected of having measles in two South London health authority districts.
With only a few children in each health authority expected to get the illness in the course of a year, it was described as significant outbreak.
Measles is potentially dangerous in a very small number of cases - it can lead to pneumonia or brain swelling
Experts say MMR can protect 90% of all children who had the first vaccination, a second dose raises the level of protection from measles to 99%.