The Shamrock Rovers players who walk out at White Hart Lane on Thursday night will be attempting to fulfil an ambition that first animated the club just over 30 years ago. Back then the Dublin side's dream of becoming a European force fuelled an enterprise that briefly promised to radically alter Anglo-Irish footballing relations, but ultimately led to a chaotic demise from which the club is only now emerging.

In 1977, the former Leeds United midfielder John Giles stunned many by resigning as player-manager of West Bromwich Albion, turning his back on the English game and returning to Ireland, to try to transform Rovers into a European power. Rovers were owned by Giles's father-in-law, Louis Kilcoyne, who several years earlier had bought the club from the Cunningham family that had presided over its golden age in the 1950s and 60s. That was before the introduction of television convinced most Irish football fans to watch British football rather than the domestic game, their interest stoked by the sights of the European Cup being won by Celtic and a George Best-inspired Manchester United. Attendances at Irish club matches plummeted. The Giles-Kilcoyne project at Rovers attempted to reverse the trend.

Rovers reasoned that stemming the flow of fans to Britain meant stemming the flow of Irish players to Britain. So they invested heavily in keeping the best Irish young players at home and also persuaded experienced Irish internationals such as Eamon Dunphy, Paddy Mulligan and Ray Treacy to return from English clubs.

"It was an exciting time," recalls Jim Beglin, the former Rovers left-back who now commentates for ITV. "The plan was first to become regulars in European competition and then push on to the next level. Giles was obviously a superstar in Ireland and was still a fine player even then – and I was to find that he was also a top-class coach and a very demanding taskmaster."

Giles sought to cultivate a stylish brand of adventurous, passing football. Rovers won the FAI Cup in Giles's first season and became regulars in Europe. Their 7-0 aggregate thrashing of Fram Reykjavik in the first round of the 1982-83 Uefa Cup is the record European victory for a League of Ireland club.

"I remember after that all the lads waiting for word of the draw and hoping that we'd be pitted against Tottenham," recalls Beglin. "We didn't necessarily think we were going to beat them but we wanted the chance to show ourselves on that stage, to test how far we'd come. But instead we were drawn against the Romanian side University Craiova, and in those days trips to Eastern European teams were quite an ordeal."

Rovers lost 5-0 on aggregate.

Giles left soon after, complaining that the Irish football establishment resented Rovers' attempt to progress and rival clubs, like crabs in a bucket, conspired to keep everyone down. A particular complaint made by Rovers at the time regarded opponents' persistence with atrocious playing surfaces, partially to sabotage Rovers' passing aspirations. Rovers' record on the road contrasted with their dominant home form.

"Maybe tricks were tried but I think we also lacked a bit of nous," says Beglin. "We played some lovely stuff but other teams with more League of Ireland experience would just edge us out in the end."

It is testament to the calibre of Giles's schooling, however, that several of the young players he coached went on to play for clubs who prized tidy football: the midfielders Liam Buckley and Alan Campbell were snapped up by Racing Santander and Beglin became Bob Paisley's last signing for Liverpool, whom he helped to the Double in 1986.

"I owe an awful lot to Rovers," says Beglin. "I was there from 16 to 19 and they gave me a brilliant grounding. When I came to Liverpool I found that they were doing pretty much the same thing that Giles had been doing in Dublin."

Rovers found success after the departure of Giles, but the full-time structure was gradually wound down and the finesse phased out. A new manager, the savvy veteran Jim McLaughlin, hired a squad of local stalwarts who won four league titles in a row.

"They had the experience that we lacked and probably played in a less elaborate way but that was what it took to win in the League of Ireland," says Beglin. It was not attractive enough to wean the Irish public off British football and attendances stayed low. In 1987, Kilcoyne tore the heart out of the club's hard core of supporters by selling the stadium, Glenmalure Park, to property developers, who knocked it down and built apartments. Rovers were homeless.

For much of the next two decades the most decorated club in Ireland club played in temporary accommodation or shared grounds with Dublin rivals. Through mismanagement and legal wrangles over a proposed new stadium, the club accumulated debts that pushed it to the brink of oblivion. In 2005 it had to go to court to argue against the imposition of a winding up order, its debts having reached €2.4m. The club was allowed to stay afloat but was forcibly relegated to the second tier. In a surprise decision, the court handed the running of the club to a group of fans who had been raising funds to keep it alive. Those fans guided the club to promotion and financial health and still run the club now.

Financial health is not, of course, the same thing as wealth. Here is a stark indication of the disparity of resources between Rovers and Tottenham Hotspur: if the Irish champions were to beat Spurs in the Europa League, a tournament of which Harry Redknapp is openly disdainful, the €140,000 prize money they would pocket would be €40,000 more than they will get if they win the League of Ireland for a second year in a row. So while Redknapp is likely to rest his best players so they can concentrate on trying to qualify for the Champions League, his Rovers counterpart, Michael O'Neill, most certainly will not, even though his team are locked in an intense struggle for the domestic title with Sligo Rovers, with whom they are level on points at the top of the table with six matches to go.

"The financial rewards we get for doing well in Europe far outweigh anything we can get domestically so that's one of the reasons it is very difficult to prioritise one over the other," says O'Neill. "Our annual budget for the entire club is around €600,000: I imagine each individual Tottenham player is on multiples of that."

The Rovers players, all semi-professionals on 42-week contracts, are not motivated merely by money, of course: the sporting thrill of toppling players presumed to be far better than them would last much longer than any win bonus.

"A lot of our squad had trials or short contracts with English clubs when they were younger and it didn't happen for them so they came home to rebuild their careers," O'Neill says. "They'll want to show that it was a mistake to let them go."

The Rovers squad does not only feature Irish players: goalkeeper Ryan Thompson hopes his performance will bring him to the attention of Jamaica and top scorer Gary Twigg is a 27-year-old Glaswegian who counts Derby County, Airdrie United and Bristol Rovers among past employers. New recruit Rohan Ricketts was once of Tottenham.

The brightest prospect, though, is probably Enda Stevens, who has agreed to join Aston Villa once Rovers's European adventure concludes. The 21-year-old is a classy left-back with wonderful crossing ability. If he makes as big an impact in England as Beglin did, you'll be hearing plenty more about him. Possibly also from him, alongside Clive Tyldesley.