The report said Blair's support for the US-led invasion of Iraq was a "terrible mistake" leading to a "debacle" that will have repercussions on policy for years.
It said: "The root failure [of Blair's foreign policy] has been the inability to influence the Bush administration in any significant way despite the sacrifice - military, political and financial - that the United Kingdom has made."
Chatham House also said that the British prime minister had been unable to prevent Britain's standing in the Middle East from sliding.
The report also said Blair had been slow to realise the consequences of a Taliban resurgence in Afghanistan on the back of drug-trafficking.
It said this was "unforgivable given the link between heroin consumption on British streets and the strengthening of warlordism in Afghanistan".
Lord Wallace, former director of studies at Chatham House, told Al Jazeera's Inside Story programme that the UK did not wield influence over the US as popular perception is led to believe.
"There is a lot of myth about how special our relationship is with the US. We shouldn't assume that we are more special than Washington's other allies," he said.
On Blair's recent visit to the Middle East, Lord Wallace, said: "It would have been a much more effective trip if Blair was visiting the Middle East representing Europe rather than being seen as the mouth piece of George Bush [the US president]."
The report concluded that Blair's successor must forge a closer relationship with Europe.
The report said: "What US governments want is an EU that can make a real contribution to the international political and security agenda, and any European government with the diplomatic skills to deliver EU support will be hugely appreciated."
|"The UK has to recognise the foreign policy role of Europe. The EU is not a single nation, there are many opinionis this can be helpful for example in Iraq."|
Volker Heise, German Institute for International Affairs
Doctor Michael Williams of the Royal United Services Institution told Al Jazeera: "Britian playing a bigger role in the EU would aid the US.
"We have all seen that a multi-lateral approach as in Europe than a bi-lateral approach is much more successful in peacekeeping and reconstruction missions."
Volker Heise of the German Institute for International Affairs told Al Jazeera: "The UK has to recognise the foreign policy role of Europe. The EU is not a single nation, there are many opinions. This can be helpful, for example, in Iraq.
"Britain, France and Germany managed to keep a dialogue going with Iran when the US was trying to block it."
Margaret Beckett, the British foreign secretary, said that the report was "ridiculously wrong."
"The notion that we don't have any influence [in the Middle East], or that we don't have any influence in the European Union, or that we don't have any influence in the United States ... is just not true," she said in a BBC radio interview.
"When it comes to the governments, the negotiators, the people who are trying to do deals, the people who are trying to bring things together ... Tony Blair's influence continues to be substantial."
Chatham House, also known as the Royal Institute of International Affairs, is a London-based independent organisation specialising in analysing international issues and current affairs.