I wasn't paying complete attention, but in Christmas Day's Call the Midwife, there were cases of measles. At least one was fatal. Local schools were closed early for Christmas and quarantine was imposed by the Board of Health.
The (US) Centers for Disease Control and Prevention reports that measles was declared eliminated from the USA in 2000. However, in the decade before vaccination became available in the USA, almost all children caught it (3 - 4 million cases annually) and 400 to 500 people died. 48000 people were hospitalised and 4000 suffered encephalitis.
Clinical Knowledge Summaries (a resource compiled for the NHS) reports that measles is rare in the UK but has become more prevalent due to a reduction in the take up of vaccination (measles being, of course, the first "M" in MMR). It is self limiting, but some complications are serious - encephalitis, panencephalitis, convulsions. Adults have more complications, so measles is a more serious condition in adults. And measles in pregnancy is a serious thing, possibly resulting in miscarriage and premature birth. Presumably these things explain why vaccination is thought necessary and why it is a notifiable disease.
Here are some resources about measles:
CDC - as well as the historical information referred to above, there is information about more recent outbreaks in the US, information for parents, including why measles is still serious (1 in 4 who get it in the US will be hospitalised, and 1 or 2 out of every 1000 will die, for starter. CDC information is also available in Spanish - there are links from some of the pages, but you can start at the Spanish home page and look for (I think!) sarampion.
CKS - information for primary care practitioners, with scenarios, and supporting evidence.
NHS Choices - information for patients, but also links to information about clinical trials.