Tony Blair personally briefed Britain's ambassador in Baghdad, with Downing Street calling almost every day as tension grew between political demands at home and reality on the ground in Iraq, the Chilcot inquiry was told today.

"The politics here demanded instant results," said Sir William Patey, who was ambassador in Baghdad from 2005 to 2006. He told the inquiry in London that the almost daily briefings from No 10 came throughout his time in Iraq.

"The first time I have ever had instructions as an ambassador directly from the prime minister was: help get a constitution that the Iraqis would vote positively for, the formation of a new government, create the conditions for the withdrawal of British troops," Patey said. "It was quite simple."

He went on: "They were quite reasonable instructions, provided you realised that they weren't in my gift or solely in the gift of the British government. There was a tension between the desire for instant results and the realities on the ground. What you could achieve in the sort of timescales that London needed for political reasons – there was a disconnect".

Referring to pressure from Downing Street to engage with the radical Shia cleric, Muqtada al Sadr, Patey said: "There was rarely a day went by when I did not have a phone call from No 10," he said. "I was encouraged by No 10 to reach out to the Sadrists to give them the message that we felt they had a place in the political system." But Moqtada had refused to see him and every Sadrist he did see "seemed to lose their job very soon afterwards … They were very reluctant to engage with us but we tried to engage with them."

Patey added: "I think the level of ambition was probably higher than the ability to deliver. What could be delivered on Powerpoint could not necessarily be delivered on Earth."

There were tensions with the US over the timing and scale of a phased withdrawal of British troops from Basra after 2006 as UK military chiefs increasingly worried about their ability to operate in two countries - Iraq and Afghanistan - at the same time, the inquiry heard.

"We did not have the means to deliver on the objectives (in Afghanistan)," said General Sir Nick Houghton, chief of joint operations at the time. Houghton, tipped as a future chief of defence staff, told the inquiry that the number of British forces deployed in Afghanistan was inadequate and Britain was not in a position to pursue a policy of "strategic coherence" there. Helicopters wanted by the British commander in Basra were sent to Afghanistan where they were also needed.

Houghton defended the withdrawal of British forces from central Basra in 2007 to their base at the airport, saying they had become the focus of violence in the city.

Simon McDonald, Gordon Brown's foreign policy adviser since he became prime minister in 2007, said the Americans had expressed concern at the speed of the planned drawdown of British forces in Iraq. "We went a little bit more slowly because that was what our key strategic ally wanted from us," he said.

Pressed by Sir Roderic Lyne, a member of the inquiry panel, about the benefits to Britain of taking part in the invasion of Iraq, McDonald said: "It reinforced our key strategic relationship with the US." It also meant Britain had a good relationship with Iraq, which was "potentially the richest country in the Middle East".