The folk rock band said that the 'Your Song' singer approached them backstage at the award show while they were getting ready to perform.
"We were getting ready and were a bit nervous, a bit sweaty" Marshall told Zane Lowe backstage at the Brits.
"Sir Elton goes, 'Winston, Winston! Come over here'. So I [went] over - I think legally we're obliged to as it's Sir Elton - and I said, 'You alright Sir Elton, what's up?'
"He goes, 'Winston, now would be a f**king terrible time to get your c**k out'."
Marshall added: "Elton John is an absolute lad. He's a hero. He made that whole thing fun, because it was so weird."
Mumford & Sons added to their awards tally at the Brits on Wednesday (February 20), picking up the 'Best British Group' accolade.
The band are said to have snubbed fellow nominees One Direction backstage at the event, with the X Factor boyband's Louis Tomlinson describing the situation as "disappointing".
Watch Mumford & Sons talk to Zane Lowe at the Brits below: