All of Europe’s 55 national football associations will gather in Amsterdam on Tuesday for an annual Uefa congress whose schedule promises routine administrative business but where the corridors will be dense with political dealing.

European football’s governing body has come a long way in the 65 years since its first congress in 1955 when the French sports newspaper L’Équipe presented its idea of a Europe-wide competition for club champions. That alluring, romantic prospect began in the 1955-56 season, 10 years after the second world war.

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The English were characteristically sniffy about the European Cup, effectively ordering Chelsea not to take part following the club’s first league championship, their only title until the post-2003 ownership by Roman Abramovich.

Matt Busby defied the Football League’s narrow-minded parochialism and took Manchester United into floodlit European competition following their 1956 title. Their need to race back and fulfil fixtures the league would not postpone was the disastrous context to the Munich air crash in February 1958.

These days the Champions League glitters as the world’s premier club competition, a stage for the greatest players, a multibillion televisual feast – and for idealists, a great exhibition put on by European countries working together. Now, though, the tournament and Uefa are approaching another crossroads, and the talk in Amsterdam will be all about the direction to take.

The intrigues lie in the convulsions administrators have got themselves into over the Champions League size and format when the agreed football calendar comes to an end in 2024. The European Club Association (ECA), the alliance of big clubs, has worked its way into the heart of Uefa’s decision-making structures but has hardly distinguished itself, coming up with a series of plans defined by no apparently coherent strategy except that there should be more matches and more money for them.

Uefa, led since 2016 by the Slovenian lawyer Aleksander Ceferin, has appeared during this process to be simultaneously dazzled, trapped and fearful. Although the threat of a breakaway superleague is low it hovers as an extreme possibility over all discussions. Uefa is newly nervous of its former general secretary Gianni Infantino, who as the Fifa president, is creating an expanded Club World Cup.

The first proposal for the Champions League was presented by the ECA and the Juventus chairman, Andrea Agnelli, almost two years ago: a reshaping of the group stage into four groups of eight that would give participating clubs eight more matches each. Last year Uefa and the ECA renewed their formal agreement, signed by Ceferin and Agnelli, that gives the ECA two elected members on Uefa’s executive committee, representation on several powerful committees and equal membership with Uefa on a joint body to consider the format of competitions.

Nasser al-Khelaifi, the president of Paris Saint-Germain and the broadcaster beIN, which buys Champions League TV rights for several regions, was elected to the exco last year, despite being under criminal investigation in Switzerland ; on 20 February he was charged with a criminal offence. He denies any wrongdoing but it is an extraordinary look for the ECA and Uefa.

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The next plan, for an expanded Champions League with 24 clubs retaining participation each season, and promotion and relegation with the Europa League, was widely rejected by national leagues and derided as a Uefa-sanctioned superleague . The latest, which will be chewed over during the dinners in Amsterdam, is reported to be a compromise: four extra group stage matches and qualification points for achievement in the previous season’s competition.

That is said to be aimed at helping successful clubs from smaller countries such as Ajax, who reached the semi-finals with those marvellous performances last season but had to start in the qualifying rounds this season owing to the Netherlands’ lower ranking. England, Spain, Germany and Italy have four clubs qualifying automatically for the group stage.

Facebook Twitter Pinterest A Uefa sign seen through a window at its headquarters in Nyon. Photograph: Fabrice Coffrini/AFP via Getty Images

Uefa’s landmark governance reform of recent years, financial fair play, has been subject to misinformed and, at times, hysterical criticism in England owing to its restraint of unlimited spending by owners but it was implemented in 2009 and has since transformed the European game’s financial health.

Ceferin was elected on a promise to address one of football’s defining fault lines, the concentration of money and success in the top clubs and the erosion of “competitive balance” for meaningful challengers.

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At the congress two years ago he promised “to fight tooth and nail” for that but there has been little sign of it since; instead Uefa has seemed more locked in an embrace with the leading clubs, to keep them as prime Champions League content-providers, and make them richer.

Above and beyond the detail of the likely formats after 2024 is a more fundamental question: about whether Uefa can be the sporting governing body European football needs at a time of unimagined success but intense inequality and challenge.