Eaton feels following the lead of the likes of cricket and horse racing and setting up such a unit would work better and hopefully prevent such criminal activity at source.
He believes prevention to be the better way of proceeding, rather than launching high-profile costly prosecutions after such scandals come to light.
Eaton spoke to Sky Sports News in the wake of the latest spot-fixing case in England which has seen six people arrested, the most high-profile being confirmed on Monday morning when Blackburn Rovers revealed their striker DJ Campbell was among them.
"I think all sports need to seriously consider anti-match fixing or integrity units of some kind," said Eaton, whose current role is as Sports Integrity Director at the International Centre for Sports Security.
"When you are commercially roaming around the world, selling sport, you are targeted by criminals. This happens in any commercial enterprise.
"There's been a global trend here, it's not just the authorities in England. Quite frankly, I think the FA and the new National Crime Agency organisation have done a great job on very little information.
"But we know this needs a close and serious global examination. You cannot rely on national agencies only in these instances, this is global crime. The source of most of these investigations seem to be coming from outside England so you need to look at this in the international context.
"They need to work together more, the whole purpose here is about preventing match-fixing and to try to disrupt these criminal organisations rather than going for prosecutions alone.
"What we need to do in sport here is to prevent fixing in the first place and take the money out of the criminals' hands, that will stop them fixing."
But author Declan Hill, whose work includes The Insider's Guide to Match-Fixing in Football, feels previous warnings have not been taken seriously enough.
He is not surprised at the recent negative headlines and feels the British authorities are way behind the rest of the world in dealing with a problem that is only going to get worse if not acted upon.
He said: "What we are dealing with now is a wave of globalised corruption that is really going to threaten the credibility of the beautiful game.
"Once this genie of doubt comes out of the bottle it's very difficult to get back in there. There will be more scandals, more news, and then three or four months down the line viewers are going to be watching matches and wondering if they are seeing a piece of theatre.
"Unfortunately British authorities have gone from denial to resignation without going through combat. What we need now is a serious look at this thing.
"People can't throw up their hands and say there is nothing we can do about match-fixing. We can start making it easy for honest players, officials, referees to report corrupt approaches. We can put in all kinds of safeguards and prevention methods.
"The problem is that British officials are coming very late to the game. FIFA, and we all know about their reputation, is far ahead of British football in terms of a proactive response to this problem.
"They have been sleep-walking their way into this problem for years. They need a proper integrity hotline set up, an anonymous hotline based on the New York Police Department anti-corruption hotline, a genuine integrity office that is well resourced and well staffed to investigate these things. They have to get their finger out and not do this in the half measures they have so far."