The crowd outside Much Wenlock Parish Church cheered as the torch, a symbol of respect and inclusion that has been part of the games since 1968, began its 200-mile journey to Sheffield, where the Special Olympics will begin on August 7.
There was a short ceremony for the lighting of the torch next to the grave of William Penny Brookes, who inspired the modern Olympic Games.
Mr Allardyce said he was thrilled to asked to join the ceremony and that it is vital all people have the opportunity to take part in sport.
“It’s important that people with learning difficulties get the opportunity to get involved in sport,” Allardyce said.
“You can see the joy on their faces at the fact that they get to take part in sports and they’re very professional and very good at it.
“It was a great pleasure to be here and to see all these smiling faces.
“To see so many people looking eager to be involved in the games after a lot of hard training and a lot of dedication is fantastic. You’ve got to give them great credit for that. There’s a great pleasure it gives everybody.
“People of all abilities should be able to compete in sports. We have to go a long way and look behind the scenes at the tremendous organisation and support that brings an event like this together, to give these youngsters this great opportunity.”
It isn’t just about participation either, Allardyce said, adding that the people involved in the games were aiming to come out on top.
“I’m old fashioned in terms of competitiveness,” he said.
“It has to be a part of life from a very young age. Participation is fine, but winning is why you enter into it.
“If you start at school and you do your English exam, you want to be the best, so why not be the best in sports? I can’t understand the mentality of the country sometimes. These athletes are in it to win it.”
The trip to take part in the event is just the latest for the former manager, who left Crystal Palace earlier this year after less than six months amid rumours that he was retiring from the game.
Allardyce said that he would never say never about returning to football, but that for now he was enjoying being out of the “aggravation” – especially when so much money is being spent in the game.
“I’m enjoying the rest time, travelling around the world,” he said.
“It’s been a great opportunity to take some time out with my family and grandchildren. I keep an eye on the football and do some TV and radio, and I look forward to seeing the new season kick off, but at this moment in time I’m glad all the aggravation is elsewhere and not with me. The difficulty for managers is the amount of money being spent. Life for a manager is ever increasingly more difficult. The lifespan you have to accept is very short – you’re in and out. There’s no longevity anymore. The old world of managers is changed. I’m here, what’s the length of my contract?
“I’ll be lucky to see it out and if I do, I’ll be moving on.
“The difficulty there is that your club spends money and every fan, everyone on social media, all the national media write about how much better that team would be by the huge amount of money that’s spent.
“You’re searching for a small percentage increase in the team, but having to pay millions, sometimes hundreds of millions, for that small increase.
“I’m not active at the moment. I can just sit back.
“If something comes along then I’ll have a think about it but for now I’ll just enjoy my time.”