Wally Edwards is tired. It is early afternoon on what should have been day five of the Lord's Test, and his usually jovial visage is clouded over with the effect of a week's meetings, lunches and dinners. He has just been out in Kensington with his wife Kerry, and is soon to leave London for Taunton and the start of the women's Ashes.

As we meet, Edwards is trying to figure out why the final round of the Open and its bevy of Australian challengers is not yet available on his television set. Weather has delayed the tournament's conclusion, but it seems strangely absent from broadcast. Cueing up my voice recorder, I tell him that the BBC's coverage isn't commencing until around 2pm.

Resigned to the fact he will not be seeing any of Jason Day, Marc Leishman or Adam Scott anytime soon, Edwards settles in to speak about the other reason he's tired: four years as Cricket Australia chairman, and near enough to two as chairman of the ICC's all-powerful Executive Committee, or ExCo. He has been widely praised for his work in the first role; almost as widely pilloried for his choices in the second.

He was mentioned in, but not interviewed for, a documentary, Death of a Gentleman, that unpacks cricket's turbulent past few years through the prism of the men in suits who preside over it. While Giles Clarke comes across badly and N Srinivasan inscrutably, Edwards isn't there at all. It is a pity, for his plain speech and happiness to debate points could have served the story well, just as it has the effective operation of CA and the ICC.

But Edwards' adamant view about the way the game is developing stands at odds with that of the documentary's creators. For a start he thinks that Srinivasan, cleared of any direct link to corruption at the now suspended Chennai Super Kings, is doing a fine job. "He's divested all his shares in CSK, so there's no issue hanging over him to my knowledge," Edwards says. "The Supreme Court [of India] came out with a positive affirmation many moons ago that he could become chairman of ICC, and that's what he is. He's doing a fantastic job."

"What we need is 20 competitive cricketing nations and then you can have a 16-team World Cup, which is the best World Cup in terms of format"

Edwards' relationship with Srinivasan began within days of his official beginning as CA chairman at the 2011 AGM. The board received correspondence from the BCCI indicating that India's 2011-12 tour of Australia would only cover two Tests instead of the scheduled four. Rather than thundering down the phone at Srinivasan, Edwards flew to Chennai in what proved a successful effort to have the tour played as originally scheduled, and thus began a relationship that culminated in the "Big Three" reforms.

The major criticism of Edwards' role in this change to cricket's governance was that he too readily went along with India rather than challenging their view of where and how ICC revenues should be distributed. He has spoken previously of the climate in which those discussions took place, and of what was at stake, but he also feels that without the changes made in 2014, any thought of evolving into the kind of structure outlined in Lord Woolf's review would have been impossible.

"We've done really poorly in the last 40-50 years in terms of developing cricketing nations," Edwards says. "You could say only really Sri Lanka has come in and been competitive. Bangladesh are showing good signs now, and that's what I've been preaching to them for the last three years: get back and get your cricket better, don't be trying to worry about opening the door to other nations coming in simply to protect your position; go and get your cricket better.

This dovetails into discussions about the World Cup, a matter Edwards has been heavily involved in.

"What we need is 20 competitive cricketing nations and then you can have a 16-team World Cup, which is the best World Cup in terms of format. You go to 14 and it doesn't quite work. To have a 14-team World Cup, you need 16 or 18 competitive nations, and I think we've got 12 at the moment. That's why a ten-team World Cup still makes sense.

Cricket at the opening ceremony of the 2012 London Olympics Getty Images

"I can understand all these nations [being unhappy], but don't forget the ten teams are the ten best teams. It's not barred to anybody, and in fact in the new rights cycle, in the third year there's no ICC event other than a World Cup qualifier, and we're hoping that will become a significant event in the broadcaster's calendar."

This qualifying event, scheduled to take place in 2018, is yet to be completely settled in terms of format. Debate has intensified over how many Full Member countries should be required to qualify.

"I hope I get my way - but I wouldn't guarantee it - which would be four Full Members having to qualify in that tournament after the first six qualify on the rankings," Edwards says. "I think that would be a fantastic tournament, a lot of interest. But I'd say the view is eight, because no one wants to put themselves on the line. That's part of the club mentality that has been there for 100 years that I've been working hard to try to break down.

"The beauty of having ICC events without having to have India, Australia, England or South Africa playing is good, because they're the teams who are overloaded in terms of their annual calendars. So to be able to bring those other nations to the top of the pile [in a qualifying event] is good."

On the subject of formats, I counter that the number of guaranteed games for India is clearly the central consideration, otherwise why would cricket be the only global sport to deliberately shrink the size of its World Cup?

"Poor old India sits there. Everyone wants them to tour and do this and that, and they do. If you did the analysis, most nations owe them games - Australia do - so they're very generous and they understand the world needs them to tour"

"The debate is a quality debate," Edwards says. "The World Cup in Australia was great, the smaller nations did okay, but really Scotland and UAE didn't do much. It was nice to have them there, but if you did the numbers, 12 of the first 39 games were between nations in the top eight. That's not ideal, I don't think. Really in a World Cup you want hard, well-fought cricket. It'd be great to have 16 in there, but we've got a lot of work to do to lift the quality.

"The reality is the world of cricket relies on India, and the discussions that are happening are: How can we grow the market outside of India? What will generate more interest outside of India. Poor old India sits there, everyone wants them to tour and do this and that, and they do. If you did the analysis, most nations owe them games - Australia do - so they're very generous and they understand the world needs them to tour."

A stumbling block for any rise in global quality is the way the ICC's global development pie has been re-cut by the Big Three. While funding for Associate and Affiliate nations has risen relative to the previous set of commercial rights deals, it has shrunk enormously as a percentage of total funding, as India, England and Australia take the lion's share of the proceeds.

Cricket's inclusion at the Olympics and its subsequent attraction by way of major government grants for major nations such as the USA and China would be a significant counterbalance to this, and Edwards believes headway might finally be made.

"Australia's position is very simple - we believe cricket should be an Olympic sport in T20," he says. "But we haven't got a majority around the board table, so that debate will go on. I think it's got to be resolved by 2017 for the 2024 games. It was good to see England make some positive comments after the MCC meeting, because they were certainly against it, because they just see it interrupting their cricket summer.

The captains, the trophy and the arena - Michael Clarke and Brendon McCullum pose for pictures International Cricket Council

"It should happen in the future, but these things take time. Debates happen, they're voted on, and if you don't win, you don't win. There's many things I've lost over the last four years, many debates, even though I think they're bloody good ideas. But we're in a conservative industry too, things don't change quickly."

Of all Edwards' ideas, the one he would most like to bequeath to world cricket is that of a calendar where every match has a reason for existing that is competitive rather than financial. His proposal for limited-overs cricket to be played to a harder ranking system for World Cups - he would like to see the 50-over game labelled World Cup CricketTM - is progressing with a view to presenting it to broadcasters for the next rights cycle.

"Realistically it would start after the next World Cup if we get somewhere, which I think we will," Edwards says. "It's rolling now, it could never have rolled without the reforms at ICC, we'd have gone nowhere. I tried debating it in the good old days and you couldn't even get it on the agenda. But now ICC are working on it, it's coming through ExCo, my committee, and I'm driving it. We had good discussion in Barbados about it."

Such a proposal would work better with a greater number of nations performing strongly and thus becoming more attractive as touring teams. The current patchwork of bilateral agreements is predicated almost purely on money, and has effectively left Test cricket, in particular, to be played among the favoured few. Not for the first time, Edwards stresses that better standards of play can drive the commercial side of the game, rather than things always being the other way round.

"It's not that simple because some nations play a lot more games than others. The FTP's there until 2023, so there needs to be changes made to that, depending on what format you settle on," he says. "The idea would be, every game you play would be going towards a table or ranking system so that every one-day game or World Cup Cricket game, which is what I want to call it, counts.

"How we're going to do it? There's a lot to be done, and nothing can really happen until after the next World Cup, but that will come around quickly."

What has come around quickly is the looming end of Edwards' term as CA chairman. Unlike Clarke, who has invented the post of ECB president to continue on at the ICC, Edwards has no desire to extend his time in the chair. Instead he is determined to give his best for whatever time he has left, and then leave the reins to others, including his CA successor David Peever. It is a lot to fit into four years - no wonder he's tired.