The British embassy said the blast targeted an embassy convoy on the airport road, close to the Umm al Tabool Mosque on Tuesday morning.
There were no injuries but an armoured vehicle was badly damaged.
A three-car convoy had just dropped off a diplomat at the US compound at the airport and was returning back to the British embassy when the explosion happened, Sky News understands.
No one has said they were behind the bombing.
The airport road was referred to during the 2000s as 'Route Irish' and back then was a well-known spot for attacks on vehicles.
British authorities do not know if they were the intended target on Tuesday and the blast has fuelled concerns over armed groups outside of the state's control.
There has been a rise in attacks against the US but this is the first IED blast on a British diplomatic vehicle in Iraq since 2009.
"The safety and security of our staff is of paramount importance and we are in close touch with the Iraqi authorities," said a statement from the British embassy.
The area of the attack, between the airport and the heavily fortified Green Zone, is often used by diplomatic missions, an Iraqi official said.
The attack is the first in months to target a diplomatic convoy and comes amid near daily rocket attacks aimed at the Green Zone and Iraqi army bases hosting US troops.
It follows a rocket attack on US and British buildings at 1am.
Two Katyusha rockets landed inside Baghdad's heavily fortified Green Zone, which houses government buildings and foreign missions, but caused no casualties or damage, the military said in a statement.
Rocket attacks against US targets have increased over the past few weeks.
Washington blames such attacks on Iranian-backed militia groups.
Iran has not directly commented on the incidents, but little-known groups believed to be connected to Iran-aligned militias have said they were behind some of the attacks.
Iraq, often the scene of spillover violence from US-Iran tensions, seeks to avoid being drawn into any regional confrontation.
The Middle East came close to a full conflict in January after a US drone strike killed Iranian General Qassem Soleimani and Iraqi paramilitary chief Abu Mahdi al Muhandis at Baghdad airport.
Iran-aligned militias have sworn to avenge their deaths.
The US military has announced that 2,200 of its troops will be withdrawing from Iraq this month.
The US has around 5,200 troops in the country that were deployed to fight the Islamic State militant group.
In June, the US and Iraq affirmed their commitment to the reduction of troops in the country, with no plans by Washington to maintain permanent bases or a permanent military presence.
The rocket attacks surged at an alarming pace when Prime Minister Mustafa al Kadhimi traveled to the US last month to conclude strategic talks.
They have put pressure on his administration, which has promised to stop armed groups acting outside of state authority.