Stoke City, who play West Ham United on Sunday at the Britannia Stadium in an FA Cup quarter-final tie, have had an albatross around their necks for the past 128 years. In 1883 the club made their debut in the competition but only they and Accrington of the Football League's 12 founder members are yet to reach the final. Of the 20 current Premier League clubs, only they and Wigan, who played their first tie 51 years after Stoke, share that stigma.

A win against West Ham would at least get the Potters a trip to Wembley, a place they last visited in 2000 for their second Football League Trophy victory, rare highlights in an often traumatic 23-year exile from the top flight after relegation in 1985. A semi-final appearance would be their first for 39 years, the last in 1972, the second failure in succession against Arsenal at that stage, which gave them the dubious honour of featuring in the short-lived and unpopular third-place play-off twice in its five-year history. They have fared little better in the league and their record makes them the biggest most success-starved club in England.

A good omen for them, however, is that they had to defeat West Ham en route to the only significant entry on a spartan roll of honour, the 1972 League Cup. In an epic seven-hour, four-match semi-final Stoke won the second replay 3-2 at Old Trafford, but Gordon Banks had to pull off a save his team-mates think rivals the one he made from Pelé for England against Brazil at the 1970 World Cup to get there.

West Ham were awarded a penalty three minutes from the end of extra-time in the second leg and the goalkeeper's fellow "Boy of 66" Geoff Hurst smashed the ball, as he always did, from the spot. "I was flying through the air with both my arms pointing skywards," Banks has said. "Geoff had hit the ball so hard that when my left hand made contact with it, I had to tense the muscles in my arm and wrist. Otherwise the ball would have knocked my hand aside. To my great relief the ball ricocheted up into the murky gloom and over the bar."

They went on to defeat Chelsea, a team who shared the same swaggering, attacking instincts, 2-1 in the final but even then reports of the match make great play of Stoke's historic lack of success. "The team they said could not win an argument," wrote Hugh McIlvanney in the Observer, "at last took one of the major prizes in a Wembley Stadium that seemed to contain half the people and all the spirit of the Potteries."

The following night the players celebrated their triumph alongside the Staffordshire miners and pottery workers in the supporters club by the Boothen End at the Victoria Ground.

That spirit of community is what endeared the club to Lou Macari who managed Stoke for two spells in the 1990s. "They are a proper club with proper fans," he says. The Britannia Stadium is noted for the sheer volume of the crowd and, as well as the good-natured bawling of Delilah, the supporters generate a ferociously intimidating air.

It was just the same at the Victoria Ground, which they left in 1997, Macari explains. "The moment the away team stepped out of the dressing room they walked into a wall of noise. As they made their way down the tunnel they got abuse. It was hostile. I liked that."

Macari was a popular figure among the supporters, but to a generation of them Tony Waddington, the architect of the League Cup-winning side, remains the club's most cherished manager. His recruitment strategy, bringing Stanley Matthews back to the club, building a later side around George Eastham, and attracting talents of the calibre of Banks, Hurst, Dennis Violett, Jimmy Greenhoff, Peter Shilton and Alan Hudson re-established the club as a First Division force in the 60s and 70s. Stephen Foster, the author of two books about his club, She Stood There Laughing and … She Laughed No More, says: "You used to go down to the Vic with the feeling that these guys were swashbuckling and that they would probably win."

Stoke had been unlucky to miss out on the league title in 1946-47 when they lost their last game, and unluckier still that the second world war robbed them of six years' service from Matthews, Neil Franklin and Freddie Steele. But it was Waddington who put the club back on the map and their barber's pole stripes became a mainstay of Match of the Day as they regularly got the better of Manchester United and Leeds at home in the 1970s. He led the club twice into Europe, but both Uefa Cup campaigns in 1972-73 and 1974-75 ended in the first round.

European football would return to Stoke if they could win the FA Cup this year, but Tony Pulis's side have been defeated twice already by West Ham this season and the team has struggled since Christmas.

There is a sense that Pulis's tactics have been rumbled after two seasons in the Premier League and among fans who travel to away games there have been murmurings of discontent. "In the first season," Foster says, "amazing things would happen. It was like a carnival. Rory Delap would throw it long and we blasted Arsenal with two Delap Scuds. Everybody goes home absolutely delighted.

"There are games when it creates joy, but when it doesn't work the purists in the crowd start saying: 'Why can't we pass the ball to each other?' But if you're bashing up Arsenal with Delap's bombs, nobody cares because the joy outweighs the aesthetic demands for something else. We are one-dimensional, but when it works it is a fabulous one."

When Stoke played at Arsenal and Fulham recently, chants of "1-0 to the football team" have rung out when City have gone behind. Pulis, though lacking charm, has not lost the fans who, in general, remain defensive about any criticism of the team's style. He is, as Foster says, two games away from taking Stoke into uncharted territory. And those who remember dark days a decade ago when Port Vale leapfrogged them and regularly inflicted defeats on their neighbours would not turn on him even if pundits think "Pulisball" has run its course.

Boring or offending the purists, but at last winning something to give the League Cup an illustrious companion in the Britannia Stadium's trophy cabinet would end a dismal record. That it may give Pulis the last laugh is a cross the idealists will have to bear.