The surrender of Mullah Rahim, the top commander for southern Helmand province, hours earlier followed the deaths of two other Taliban leaders in recent weeks.
"The Taliban's senior leadership structure has suffered a shattering blow," Lieutenant-Colonel Robin Matthews, a British army spokesman, said in the statement on Tuesday.
Three other fighters had also died in the air strike, added the statement.
Elsewhere, US-led and Afghan forces backed by air strikes killed or wounded at least 30 Taliban fighters in western Afghanistan, the regional police chief, Ikramuddin Yawar, said on Tuesday.
Yawar said the toll in the fighting which broke out in the Bala Boluk district of Farah province was likely to be higher "because the operation is ongoing".
Also on Tuesday, a US-led convoy was hit by small arms fire and rocket-propelled grenades in Bala Boluk, a US army spokesman said.
In the central province of Ghazni, four brothers who were Afghan police officers were killed in an attack on their home late on Monday. Their father was also captured.
The interior ministry in a statement blamed the attack on the "opposition", a reference to the Taliban and other fighters the government says are trying to destabilise it.
In Khost province on the border with Pakistan, at least four people were killed, including a woman and child, when a remote-controlled bomb exploded underneath a pick-up truck.
Colonel Mohammad Yaqoub Mondozai, the deputy provincial police chief, said three other people were also wounded in the blast.
In the capital Kabul, a suicide bomber blew himself up, wounding five people, the interior ministry said.
There was no claim of responsibility for the attack.