Ukraine has seen 173 measles cases so far this year and the UK's Health Protection Agency (HPA) expects the 'large' outbreak to accelerate.
The UK has also seen a sizeable outbreak this year, centred on Merseyside. HPA figures show cases have risen 22% so far in 2012 and now stand at 446, far surpassing the 367 reported in the same period in 2011.
An HPA statement said: 'Measles is beginning to re-emerge in regions where there were no cases previously or very small numbers with clusters reported from the East of England, the West Midlands and London.'
On the situation in Ukraine, the HPA said: 'There have been vaccine shortages in Ukraine since 2010 and more than one million children are unvaccinated, therefore the epidemic is expected to accelerate and spread geographically during the measles peak transmission season from February to June.'
It added: 'The European Football Championship will be jointly hosted by Ukraine and Poland in June 2012 and visitors to the event are encouraged to ensure they are fully vaccinated.'