Allardyce says that all UK sports, not just football, are suffering because of policies adopted by Thatcher's Conservative governments throughout the 1980s.
In a scathing attack in The Sun newspaper on Saturday, Allardyce said: "Since Margaret Thatcher stopped teachers being paid extra money for coaching sports after school, all sporting activities have diminished on a competitive basis.
"Kids are now more obese and unfit than ever. All the prime young athletes we were ready to develop just aren't there, so we get a lesser quality of player.
"It has not just undermined our game, it has undermined many sports in this country and created an unhealthy child. Thatcher killed football, there is no doubt about it."
A recent report stated that one in three children in Britain are obese or overweight and that 32 percent of children play less than an hour of sport a week.
In the last 20 years, around 5,000 school playing fields have been sold off or built over as England's men's national team have continually floundered in attempts to repeat their 1966 World Cup triumph.
Allardyce, a keen student of sporting education, continued: "Look at how little kids do to what I did. I was a 200 metres runner, a 4x400m relay runner and a triple jumper.
"I was a batsman in cricket, a freestyler in swimming and swam for the town. I did the pommel horse in gymnastics and I was really good on the trampoline, as well as being a footballer.
"Kids don't do any of that now. All of that sporting activity allowed me to play in the top division in this country."
Allardyce, who recently took over at West Ham, maintains the consequences of Thatcher's policies now mean clubs are having to sign up children at increasingly young ages to ensure they have opportunities to flourish.
"This was a working-class game but it's only at private schools where the children get the sports opportunities I had - and even then a lot of them don't play football, it's mainly rugby," said the ex-Bolton Wanderers and Blackburn Rovers boss.
"Despite putting in place all sorts of advanced academy systems at clubs we are only producing half the players the school system used to."
The Football Association estimates it takes 10,000 hours of training and education from the age of about seven or eight to be able to be good enough to play professional football - accepting a child has the talent to begin with.
Allardyce added: "Even a club like Manchester United can only provide 4,000 hours at the moment. It's hard to do more because parents have to drive their kids there four nights a week as well as on a Sunday.
"Until we wake up and realise how important school sport is to our kids we will never repair the damage," he concluded.
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