As Hopkirk indicates, the live and neutral terminals within a 3-pin socket are protected by a plastic screen. (That's to reduce the risk of electrocution if, say, a toddler was to push something into the socket).
When you insert a 3-pin plug, the top (earth) pin pushes that screen to one side, enabling the other two pins to then go into their respective places. (That's why the earth pin is longer than the other two; it has to do its 'shoving aside' trick before the other pins can go in).
So, without an earth pin present, you shouldn't be able to get the other two pins inserted into the socket anyway.
Cut the old plug off and fit a new one!