Not 100% voted.
There have actually multiple referenda in recent years, but they've mostly been to specific regions. There was on independance in Northern Ireland, for example, plus the devolution referenda in Scotland, Wales, and later the North East.
I have to say, referendums do have some problems, but I see some use for them. The EEC one for example, I consider one of the few accomplishments of Wilson's time in office (not to mention of the few promises he actually lived up to).
Oneyedvic's criticisms all hold true, but I think there are some issues from time to time which the populace simply should be consulted on (like the EEC one). Obviously not everything can, and it's fallacious to try - but I think there is a welcome place for referendums used correctly.
Governing by referendum though, would be an absolute disaster. The issues which people have pointed out (such as immigration) are actually highly divisive and could also lead to what Mill called the 'tyranny of the majority'. Oversimplifying on such issues wouldn't help the situation at all and might not be so clear-cut as people think. In which case, you'll have just wasted a load of money and time, and people - being people - will likely blame the government.
There is an interesting idea, however, for an oppurtunity for direct democracy to work in this day and age with heightened levels of instant communication allaying the demographic problems. To be honest, I personally think it would be a disaster (and I also think people wouldn't like to have to blame themsevles), but it's still interesting.