I say this after watching some of the brilliant FIFA Women's World Cup. The skill shown by many of the teams is fast approaching that of the men.

The women's game has improved beyond all recognition these past few years as indeed it has in other sports including rugby and cricket. Okay, so it may happen later rather than sooner, but peering into the pages of Old Hubbard's Almanac I see World Cups and championships say, in the 2070s or 2080s, featuring teams not only of mixed races, as they do now, but of mixed sexes. Certainly before the end of the century.

I emphasise that here we are talking about games involving skill rather than sheer strength and muscle power. As diets, technique and training methods improve, so will women's sport. But of course there is still a way to go, baby.

Even in contact sports such as boxing, taekwondo, karate and judo, men and women are pitted against one another in training sessions. I know this for fact as a few years back I saw my daughter, a black belt, throw a much heavier bloke over her shoulder many times.

Who is to say that will not be translated to the ring and on the mat in the lower weight divisions of these activities?

Is this a feminist pipe dream? I think not. When I first watched women boxers in a training session at Crystal Palace it was handbags at three paces. Now the likes of Katie Taylor, Clarissa Shields, Nicola Adams and others spar with men and could certainly hold their own in the club competitions against male counterparts.

Rugby, we know, can be pretty rough. Some say it is not a game for girls at all. But we have seen differently in recent internationals and I reckon that while we are unlikely to see women in the scrums, there are women athletes in the world who are fast enough and powerful enough to be on the wings or be scrum halves or fly halves.

Matches composed of male and female cricketers together? Why not? The world is being transformed. Anything is possible whether it is business, industry, politics or sport. And glass ceilings are being shattered all over the place. Indeed, the fact we have to mention this these days seems rather sexist in itself.

How long will it be I wonder before we have women umpires adjudicating in men's games in cricket or a female referee officiating in an FA Cup final? You may scoff or snort in derision but would you bet against it happening in a couple of decades also? I wouldn't.

Some of my more misogynist mates reckon my thoughts are at best fanciful and at worst laughable. But I fancy it will be me – and the ladies – having the last laugh.

Nor will I bet against a woman ever becoming the head of that most sacrosanct of old boys clubs, the International Olympic Committee. Or indeed FIFA.

Girls will be girls and boys will be boys we used to say. Not in sport any more. And I'm not talking about transsexuals or those with an excessive amount of testosterone in their bodies. That is another matter altogether.

Equality already exists in some areas where perhaps it should not. Tennis, for example, where women now receive the same prize money at Wimbledon as men even if they may well spend a much shorter time on court. That could easily be adjusted by making them play five setters too, especially as they no longer regard themselves as the weaker sex.

Of course those of us of a certain vintage are unlikely to be around by the time all this happens. Mind you, it may not happen at all if any of Messrs Trump, Bojo, Putin, Kim Jong-un and whichever mad mullah may in charge of Iran at the time punches the button which blows Mother Earth off its axis.

Olympic sports such as a equestrianism, shooting and archery already have integrated teams, more will follow and I expect the Games to adopt mixed relays on the track.

Female jockeys are now showing that they – and their horses of course – can beat men who occupy the saddle. Similarly I doubt it will be too long before we see women lining up with male counterparts on the grid in Formula One.

Or am I being over optimistic? Better that than chauvinistic.