To be fair, measles probably stopped being ghastly in this country for long enough that most people no longer saw or knew the risks from personal experience. Look at Islay's post, for example: an entire family affected by measles but apparently shaken off rather like Chickenpox would be.
We can be very complacent about certain medical conditions. It comes from a good place, as it's a direct consequence of generally fantastic healthcare. But it's also rather a sad one when it leads to dodgy risk assessment, as happened in the MMR scare of the 90s. If you can see autism with your own eyes, but can't see measles (because it has been basically absent from the UK for a few decades) then you'll fear the one you can experience more than the (more serious) thing you don't. No one can get past that: it's just the human condition.
At the moment it seems that MMR uptake is close to maximal in the UK, but now Wakefield's dodgy stuff has passed to the US to be taken surprisingly seriously there, instead. So Measles might re-emerge from time to time in the US, for the same basic reason.
Humans are just really bad at understanding risk assessment, basically.