A brace from Roland Sallai and further goals from Zsolt Nagy and Daniel Gazdag condemned the Three Lions to a humiliating loss that was greeted by full time boos.
England have finished their four-game post-season Nations League run without a win, twice tasting defeat against Hungary, the world's 40th ranked team.
John Stones compounded England's misery with a late red card, but with 10 men or 11, the Euro 2020 finalists were out-classed in a watershed moment for Southgate.
The defeat is England's heaviest at home since 1928, and they did little to stop it coming, registering just two shots on target while Hungary created five with ease.
Supports had already grown frustrated with draws against Germany and Italy, but there were positives to take in those previous fixtures, however, any excuses had dried up after defeat to Hungary.
Southgate already has a huge issue to deal with in defence with one of his stalwarts, Harry Maguire, struggling for Manchester United, but his solution of John Stones and Marc Guehi completely failed.
talkSPORT commentator and West Ham coach Stuart Pearce was in shock when Sallai was gifted an early opener, holding Stones responsible.
"Stones has dropped much too early and created panic. The pace on the ball from close range gives [Aaron] Ramsdale no chance," he said.
"That's a real worry for me, John Stones dropping off so deep. You just cannot do that to your teammates. You will play everyone onside. That's something that will cause concern going forward."
Those concerns were held off until half-time despite boos which talkSPORT's Adrian Durham described as 'generous' but things soon took a turn for the worse after the break.
Sallai grabbed his second with 20 to play as he poked home after some lapse play from Kalvin Phillips, and then it was three as Nagy brilliantly smashed the ball home with England's defence all over the shop.
And just when things couldn't get any worse, they did.
"That's the worst booking I've ever seen," said Pearce as Stones left an elbow out for an unnecessary second yellow, leaving a space for Gazdag to cap off the humiliation minutes later.