There was a time, not long ago, when all that mattered to the East Yorkshire club was actually prospering by any means necessary at the iconic stadium.
Such was Hull’s wretched record there, they failed to win once in eight successive attempts at the national stadium.
After 87 years of trying, they finally achieved it as Radford’s side famously beat Warrington Wolves 12 months ago to leave their long-suffering fans in a state of ecstasy.
They will seek to retain the trophy when facing Wigan Warriors – the Super League champions who are slight favourites – this afternoon, but that alone will not be enough in the coach’s eyes.
He, of course, was involved when abject Hull were whitewashed 16-0 by Wigan four years ago in arguably the worst final in all of the competition’s 121 years.
In contrast, that was the first time the rivals had met at Wembley since the glorious 1985 affair when, with Australian legends Peter Sterling and Brett Kenny facing each other, Wigan won 28-24 in an epic contest.
Indeed, it is still widely regarded as the greatest Challenge Cup final. Understandably, the 2013 meeting was built up beforehand in the hope of a repeat only to turn into a rain-drenched, error-ridden debacle.
Asked if he cares whether today’s performance is more akin to the glittering fare of ’85, Radford told The Yorkshire Post: “Actually, that is important to me. It genuinely is.
“I watched that game again a month ago on YouTube. It is important to me that this is a spectacle just like that was.
“I was involved in ’13 as an assistant coach and it got voted the worst Challenge Cup final of all time. That does not sit right with me at all. It really doesn’t. So, not only do I want to win, but I want it to be a real spectacle as well.”
Hull looked relaxed yesterday for the Captain’s Run, the traditional eve-of-final visit to Wembley, often including a light practice session, that allows sides to acclimatise to the surroundings ahead of the main event.
Clearly, though, an empty stadium does not truly prepare anyone for returning 24 hours later and walking out into a cauldron of noise created by an expected crowd of around 65,000 people.
The Black and Whites fell 10-0 behind against Warrington last year, perhaps caught up in the occasion themselves.
However, Hull-born Radford hopes they will start better against the World Club champions this afternoon.
“I just think mentally for the players, hopefully they’ll be a little more relaxed this time around,” said the 38-year-old, who won the Cup once as a player with Bradford Bulls at Cardiff in 2003.
“What tends to happen in finals – all major finals – is you play the game in your head 80 million times before you go to bed and you use so much nervous energy before you even start.
“I remember last year (second-rows) Sika Manu and Mark Minichiello – who had comfortably been doing 80 minutes for us all season – were giving the message up to us just 10 minutes in that they were needing a rest.
“Ninety-five per cent of that squad will be running out again on Saturday, though. Hopefully, they’ll be mentally a little bit better off for it.”
It is somewhat surprising Hull are underdogs – they get a two-point start with most bookmakers – given they have already beaten Wigan twice this season and sit third in Super League, four places above their rivals.
However, that perhaps illustrates Wigan’s improving league form and the number of high-class internationals they now have back fit and firing.
Furthermore, they have won the Cup 19 times, more than any other club in history.
Meanwhile, Radford – who selects from strength – has highlighted England stand-off George Williams as Wigan’s key threat.
“I think one area we have to be really good at this time around is defending their kicking game,” he said.
“Their short kicking game is the best in the competition, particularly with George.
“He forces so many back-to-back sets it’s like he’s got it on a string at times. If you look at their tries all through the season, about 60 per cent are coming from short kicks.
“The job we do defending that on the day is going to be really, really important for us as it’s going to be a huge threat from them.”