A book I have on English monarchs says that he was killed by an outlaw named Leofa, but it doesn't go into any more detail. Some light googling has only yielded a little more info. Who was Leofa, and why/how did he kill Edmund?
Wikipedia is reasonably well-sourced for once, TL;DR - popular legend has him killed in a brawl at a feast.
On 26 May 946, Edmund was murdered by Leofa, an exiled thief, while attending St Augustine's Day mass in Pucklechurch (South Gloucestershire).[7] John of Worcester and William of Malmesbury add some lively detail by suggesting that Edmund had been feasting with his nobles, when he spotted Leofa in the crowd. He attacked the intruder in person, but in the event, Leofa killed him. Leofa was killed on the spot by those present.[8]
Cite 7 says:
"Here King Edmund died on St Augustine’s Day [26 May]. It was widely known how he ended his days, that Liofa stabbed him at Pucklechurch. And Æthelflæd of Damerham, daughter of Ealdorman Ælfgar, was then his queen." Anglo-Saxon Chronicle, MS D, tr. Michael Swanton.
Cite 8 says:
"But William, libro ij° de Regibus, seyth (says) that this kyng kepyng a feste at Pulkirchirche, in the feste of seynte Austyn, and seyng a thefe, Leof by name, sytte [th]er amonge hys gestes, whom he hade made blynde afore for his trespasses – (quem rex prios propter scelera eliminaverat, whom the King previously due to his crimes did excile) – , arysede (arrested) from the table, and takenge that man by the heire of the hedde, caste him unto the grownde. Whiche kynge was sleyn – (sed nebulonis arcano evisceratus est) – with a lyttle knyfe the [th]e man hade in his honde [hand]; and also he hurte mony men soore with the same knyfe; neverthelesse he was kytte (cut) at the laste into smalle partes by men longyng to the kynge." Polychronicon, 1527.