Dunn was a member of the side which beat Leicester City at Wembley and his passing leaves Sammy Smyth as the only survivor of Stan Cullis' side from that April.
Born in Edinburgh and raised in Liverpool, Dunn joined Wolves as an apprentice in 1941 turning professional the following year.
He made over 100 appearances for the club in wartime football before making his full debut against Middlesbrough at Molineux in November 1946.
The following two seasons saw him making 54 League appearances and a further nine in the FA Cup before he missed much of the 1949/50 campaign with a back injury.
He joined Derby County for a £15,000 fee in 1953 by which time he had scored 40 goals for Wanderers from 144 League and Cup appearances including an outing in the FA Charity Shield against Portsmouth at Highbury.
After leaving Derby in 1955, he went on to play non-League football for Worcester City and Runcorn and, on retiring from the game, he ran a pub in the Penn district of Wolverhampton.
He later qualified as a physiotherapist and became a trainer at West Bromwich Albion, taking a place on the Baggies bench at Wembley in the 1967 League Cup Final and 1968 FA Cup Final.
"We were all saddened to hear that Jimmy had passed away this morning," said Wolves CEO Jez Moxey.
"We kept in close touch with him in recent times and only this summer he came back at have another look around Molineux.
"We send our sincere condolences to all of Jimmy's family and friends, as we remember another of our players to have made a key contribution to the club's history."