ECB chief executive Tim Lamb told a news conference at Lord's: "The decision of the management board was unanimous.
"We have not been elected to make decisions of a political nature."
He added that all the England players had said they are ready to play in the February 13 game as long as it is still regarded as safe.
"They are happy to fulfill their obligation to play in this match," he said. "There is no indication any player wishes to withdraw."
Five days ago Culture, Sport and Media secretary Tessa Jowell told the ECB that the government opposed the match in Harare against Zimbabwe because of security concerns and what she called the appalling human rights record of President Robert Mugabe's government.
Lamb blamed the government for a "policy vacuum" in trying to force cricket to make "a unique and unilateral sacrifice" while not stopping British companies from trading with Zimbabwe, a former British colony.
Lamb, though, said England would not take part in any official ceremonies which could be seen to endorse Mugabe.
The conference was delayed for almost two hours by protesters who barged past security officials, displaying placards saying "Bowl out killer Mugabe", "No cricket while Zimbabwe burns", and "Berlin 1936, Harare 2003".
The group was led by British activist Peter Tatchell, who has twice tried to perform a citizen's arrest on Mugabe.
"We are not going to sit idly by while people are starving," Tatchell said, comparing the proposed trip to Britain's competing at the 1936 Berlin Olympics which Nazi dictator Adolf Hitler used to glorify his political beliefs.
Australia, Pakistan, India, Namibia and the Netherlands are also scheduled to play in Zimbabwe. The World Cup, which will be staged in South Africa, Zimbabwe and Kenya, opens in Cape Town on February 8.
The Australian government has also opposed the games in Zimbabwe but, like its British counterpart, has said it would not force its national team not to play.
Lamb re-iterated the ECB would face heavy fines if it broke contracts to play the match and said it was "bizarre and unfair" the British government had not offered to help with compensation.
