Sally Munday, chief executive of the England Hockey Board, added: "The EHB's desire to host the 2014 World Cups is part of a long-term strategy to help drive up the profile of our sport across the UK.
"Hosting the 2014 World Cups would provide another opportunity to engage with the 630,000 hockey ticket holders from London 2012 and we are working with the hockey community to prepare for a real increase in participation in our sport."
The bid has the financial backing of UK Sport and Events for London, who will inject £980,000 and £500,000 respectively should it prove successful.
A successful bid would see Warren, who is Britain's most high-profile boxing promoter, lead the promotion and ticketing for the World Cups.
England last hosted a World Cup in 1986, when the men's tournament was held in Willesden, north-west London. England finished second, their best performance.
Mayor of London, Boris Johnson, said: "Staging the Hockey World Cups at the new state-of-the-art Lee Valley Hockey Centre in 2014 would be a major boost to the great sporting legacy we are striving to achieve following the 2012 Games.
"I'm fully behind the England Hockey Board's bid and I'm certain it will inspire many more youngsters to become skilled players at our fantastic new facility in the Queen Elizabeth Olympic Park."
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