The topic has come under increased scrutiny in England following the arrest of six people over allegations of spot-fixing in an investigation by the National Crime Agency (NCA), including Blackburn Rovers striker DJ Campbell.
Horne attended a meeting of British ministers in London including culture, media and sport secretary Maria Miller and representatives from football, cricket, tennis, rugby union, rugby league and the British Horseracing Authority (BHA).
And Horne stated after the meeting that he believes corruption is not widespread in football, while also warning against "complacency" in tackling the problem.
"I think the general consensus around the room was this isn't a big issue," he said. "The intelligence that we have says it isn't a wide-scale issue at the moment but, again, we don't want to be complacent.
"It's clear that, as Britain, we are very proud of our sporting product, of the sport that we play in this country and we all want to do all we can to protect the integrity of that sport.
"We are never complacent on this issue and there's a lot we can learn from other sports. Some of the education programmes that cricket have put in place are very far advanced, and the integrity that the BHA have in place is very far advanced so there's lots of learnings that are open to all sports.
"We don't want to see this in our sport and so, therefore, we are doing everything we can, we are looking at all measures we can across sport but also with the agencies.
"We really welcome the recent impetus from the NCA. I think that is going to be a really important body for all of us in reminding people that these are criminal activities and the criminal nature of activities shouldn't be underestimated and all power to the NCA."