In a statement from London on Friday, Foreign Secretary Jack Straw said Britain was "consistently in the lead in seeking to enforce sanctions against Iraq" when Saddam Hussein was in power.
But he stressed that enforcing UN sanctions was the responsibility of Iraq, all other UN member states and the UN administration.
"There were no occasions which we can recall on which the United Nations made representations to the United Kingdom" with regards to sanctions-busting smuggling activities, he added.
Annan - whose son was implicated in the oil-for-food controversy – on Thursday said Britain and the US knew about the wrongdoing but turned a blind eye.
"Possibly they were the ones who knew exactly what was going on, and that the countries themselves decided to close their eyes to smuggling to Turkey and Jordan because they were allies," he said in New York.
Annan accused US and Britain of
Straw said suggestions that Britain ignored smuggling of oil from Iraq to Jordan and Turkey were inaccurate.
"The United Kingdom was consistently in the lead in seeking to enforce sanctions against Iraq," he said in a statement released by the Foreign Office.
"The fact that the smuggling of oil was most likely to take place to Turkey and Jordan simply reflects the geography of the area."
"Jordan and Turkey have land borders with Iraq. Jordan and Turkey were primarily responsible for preventing smuggling across their borders," he said.
He pointed out that in May 2001, Britain had drafted a UN Security Council resolution "seeking to clamp down on smuggling through providing lawful supplies of Iraqi oil to Jordan and Turkey, but this resolution was opposed".
In New York, the US mission to the United Nations distributed testimony its chief of staff Thomas Schweich had made to the US Congress.
"The fact that the smuggling of oil was most likely to take place to Turkey and Jordan simply reflects the geography of the area"
UK foreign secretary
Schweich said the Security Council's 661 committee overseeing the programme as well as Congress allowed the exports to Jordan and Turkey, and were open about it.
He said this was not analogous to "the bribery, the corruption, the kickbacks, the things that were done for self-interest secretively in a non-transparent manner that are really just acts of fraud and crime."
UN spokesman Fred Eckhard denied Annan was shifting the blame to the Security Council. He said Annan had consistently said "he shared responsibility" with the 661 committee.
British oil trader charged
Meanwhile, the British oil trader indicted in the United States on Iraq-related corruption charges denied wrongdoing on Friday.
In a statement released by his lawyer, John Irving said he was surprised and horrified by the allegations.
On Thursday, US officials charged Irving, Texas oil executive David Chalmers and Bulgarian oil trader Ludmil Dionissiev with paying millions of dollars in secret kickbacks to Saddam Hussein's government to secure oil deals.
The US authorities said they would seek the extradition of Irving, an employee of Chalmers' Bayoil firm.