Goals from Raheem Sterling, Harry Kane, Harry Maguire and Declan Rice gave the Three Lions a fourth win in four in this campaign as they aim to move on from July's Wembley heartbreak against Italy.
An England side showing only one change from that penalty shoot-out defeat – Jack Grealish in for Kieran Trippier – dictated play in Budapest, but had to bide its time.
Sterling took his chance early in the second half, though, and Gareth Southgate's men were comfortable thereafter, the outing only marred by objects thrown from the home supporters during England's celebrations as they moved five points clear at the top of Group I.
England had waited until the 50th minute for its first clear-cut opportunity, which Kane then uncharacteristically squandered, scuffing his finish and allowing Peter Gulacsi to block after an incisive Kyle Walker pass.
But the visitor soon carved Hungary open again and Sterling was less forgiving, steering into the bottom-right corner from Mason Mount's cutback.
There was no way back for Hungary when Mount and Sterling combined again and the latter's driven cross deflected off Attila Szalai onto the head of Kane, who this time did not disappoint.
Gulacsi was able to deny Kane again as Grealish led a counter on the left, but the goalkeeper was less impressive moments later as Maguire's header squirmed into the net, further rewarding a patient first-half display.
A bizarre display from Gulacsi was complete when he recovered a tame Sterling finish after the forward had set up an open goal and then blocked once more from the profligate Kane, only to let Rice's straightforward shot beneath him.