Neither of the shoes hit the president who was flanked by his host, the Iraqi prime minister Nuria al Maliki, at a news conference the two men were addressing.
The British press reported that Britain intends to begin withdrawing troops in March with most out by June, although defence officials insist the precise timetable will depend on conditions on the ground at the time.
Britain has around 4,100 troops in Iraq, based at Basra airport outside the southern oil port city.
They are training local troops but retain the capacity to intervene if required by Iraqi forces.
Brown's visit comes after the Iraqi cabinet approved a bill calling for all foreign soldiers except for American forces to pull out of the country by the end of July.
Citing a senior defence source, the BBC and The Times newspaper said the pullout was planned to begin in March - six years after the US-led invasion of Iraq - if provincial elections set for the end of January passed off peacefully.
The Ministry of Defence did not deny the reports.
"We plan - subject to the conditions on the ground and the advice of military commanders - to reduce our force levels in Iraq as we complete our key tasks in Basra in the early months of next year," a ministry spokesman said.
But he added: "Final decisions on the timing of the drawdown will depend on the circumstances at the time.
"We will remain committed to Iraq. We expect to move from next year towards a long-term, broad-based bilateral relationship with Iraq similar to the relationship we have with other allies in the region, including a training and education role for our military personnel."
British commanders had intended to reduce troop numbers to 2,500 earlier this year, but conditions on the ground prevented them from doing so.
On his last visit to Iraq in July, Brown spelled out four objectives to be completed before British troop numbers could be reduced.
These were finishing the training of the Iraqi army in Basra, transferring Basra airport to civilian use, aiding local economic development and providing support for the January 31 election - the first vote in the country since 2005.
On his return, he told British parliament that he expected a "fundamental change of mission in the first months of 2009" but he expressly ruled out setting a timetable for their withdrawal.