Children can be vaccinated against these diseases by a series of six separate injections.
The UK used to use single vaccinations for measles until 1999. The government stopped this because experts didn't think the single vaccination gave as good protection as MMR.
But many worried parents now want the government to bring in the six single injections instead of the combined MMR jab.
The government are worried that many parents might forget to finish the course of six vaccinations.
And now because of the worry over the MMR, many children aren't getting the jab. This means lots of kids are unprotected from these diseases and there could be a measles epidemic.