Ireland winning the World Cup.
Think the issue is that with England it's very tribal. It's your region (or more specifically club) before anything else. When the English players get together there is divisions due to their club affiliation. To use just one example, Scouse and Manc players aren't excactly going to be best mates. Same applies to fans...Mancs cheering on a Scouser (red side), or a Scouser (red side) cheering on a Manc (Gary Neville), it's not going to happen. Or even a blue Manc cheering on a red Manc, again, no chance. Harry Kane scoring the winner for England would sicken many English Arsenal fans. Sir John Terry (which is what we would have become) lifting a trophy would have sickened most of England outside Stamford Bridge.
Always felt the most important quality needed by an England manager was man management. An ability to instill a bond among the players. England generally play like strangers. The 'golden generation' played like a group of individuals. Can barely recall a good game they all played in, yet for their clubs, different story. They looked uncomfortable around each other on and off the field. Hiring Eriksson and Capello with their pidgin English was distastrous. They were never going to get the players playing as a unit. A Harry Redknapp would have done a far better job. Tactically he's not on the same planet as Capello, but he would have got the players playing together. Players under Ferguson have repeatedly stated his best quality was man management. Brian Clough didn't train the players. It was 100% man management with him. England have had top players, but they played far below themselves as there is no cohesiveness. There's also a selfishness as a player will want to do well for himself to avoid getting hammered in the press. Taking a shot at goal rather than play in someone in a better position..and goal scorers running off into the corner rather than going straight to a teammate. The press is a huge factor in this. Players look frightened, inhibited. Andy Cole showed nowhere near his ability in an England jersey, which also applies to 90% of the players. Teddy Sheringham not shaking his hand when he came on...it's just not a team. That's the crux, England are not a team. Robson and Venables came the closest in recent times to making it one.
With Ireland we don't need a man manager to bring all the players together. They are already united. When they put on the green jersey club affiliations go out the window. Robbie Keane at Spurs, Duff at Chelsea, didn't mean a thing when they were with Ireland. This also applies to fans. Couldn't give a stuff what club anyone played for I was 100% behind them in a green jersey. English fans of lower league teams aren't affected by the tribalism of fans of the top English sides whose players are in the England team...so a Shrewsbury fan will cheer all the England players.
After underachieving for decades due to a similar issue Spain has managed to overcome this regional tribal handicap to have great success, though the main reason they did is they had an inbuilt unit from Barcelona. Busquets, Xavi and Iniesta in midfield (plus another Barca youth product in Fabregas and also a player who gets on with everyone in Xabi Alonso). At the back it was Puyol and Pique, so the spine was already there. Much easier to add Sergio Ramos and Casillas to this than trying to put together a group of individuals. Effectively the Barcelona youth system won the World Cup for Spain. Without that inbuilt spine Spain would have continued to underachieve like England do.