Playing down any idea that England were favourites to win the right to host the event, he said with 11 nations competing for the votes of just 24 FIFA Executive Commitee members, it was impossible to say who was likely to win.
As well as England, there are bids from Spain, Russia, Australia, the United States, Netherlands-Belgium, Qatar, Indonesia, Mexico, Japan and South Korea for either 2018 or 2022.
FIFA will announce the hosts for the two tournaments in Zurich in December next year and Anson told a news briefing in London that while England represented a safe pair of hands other countries also had selling points.
"There are 11 countries ultimately bidding and they are just as desperate to win as we are," he said.
"That makes it incredibly challenging and that's why we cannot be complacent. Any talk about England being favourites is slightly misplaced because it's so competitive.
"I don't think we are going to be the only ones who feel really passionate about winning.
"It's going to be an incredibly tough race and that's why we have to work extra hard to make sure our messages are very clear."
One message that England could put across was that they had "great infrastructure, great stadiums and the real passion of the fans," which would all guarantee a successful tournament, Anson said.
SOCCER CULTURE
He added that UEFA president Michel Platini was a great admirer of England's "soccer culture", which permeated into the very core of the national culture. Platini's stated ambition is to ensure the 2018 World Cup is staged in Europe.
Anson added that England, which last staged a World Cup in 1966, also needed to stress it could promise international development programmes as a legacy of a World Cup.
"We are a very attractive commercial proposition, we have great stadiums in this country, and an overseas legacy programme would have a huge impact," he said.
"A safe pair of hands can quite often be a negative thing but to be viewed as someone who is reliable with great facilities, great infrastructure, and great stadiums is a very positive thing.
"There are challenges with the next two World Cups. FIFA have been very adventurous in going to South Africa and Brazil and I think that we have the infrastructure in place where we can deliver a World Cup much more easily."
But Anson said any repeat of the hooligan violence which blighted West Ham United's League Cup match with Millwall last week could damage the bid.
He said: "It was incredibly disappointing. It seemed like an isolated incident and we certainly hope it was an isolated incident.
"Obviously if there was a repeat of it, it would be damaging, and I think everyone has realised it's not something we can let happen again.
"It has been recognised by FIFA and UEFA that England has done an awful lot to address this problem over the last few years."
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