The prime minister has said George W Bush's visit to Britain was a "fantastic opportunity to think about this relationship between Britain and the United States".

Tony Blair was speaking at the end of the US president's four day trip which concluded on Friday

"People sometimes talk about this alliance as if it was some scorecard," he said.

"It isn't, it's an alliance of values, it's an alliance of common interests and convictions and beliefs."

The comments came as President Bush brought his state visit to Britain to a close.

The Queen formally bade farewell to the US president and the first lady on Friday morning.

George W Bush then travelled to the prime minister's Sedgefield constituency, where the two men lunched with selected members of the public, before flying back to Washington.

Assessments will now be delivered on what the first state visit to Britain by a US president has achieved.

Although Thursday saw a series of discussions on a range of issues, there have been no significant agreements.

And the trip has been overshadowed by the terrorist attacks in Turkey and protests about the war in Iraq.

The prime minister and the president held an hour-long meeting on Thursday at which Iraq, world trade, HIV and the Middle East peace process topped the agenda.

Following the meeting Bush pledged that the two countries would "meet the new challenges" of the 21st century.

The prime minister said his resolve was undiminished following the terror attacks in Istanbul.

"It is in a free, democratic and stable Iraq that not just the violence, but the wretched and backward philosophy of these terrorists will be defeated and destroyed," he said.

The prime minister also revealed that both men aimed to "take forward" the issue of freeing world trade.

Both men also made clear there would be no immediate announcement on the fate of the British prisoners held at Camp Delta.