The soldier and children were killed in a suicide blast in the southern town of Lashkar Gah, capital of Helmand province where most of the 5,000 British troops in Afghanistan are based, the Nato-led force and Afghan police said.
The suicide attacker launched himself against a British patrol in the town. Two British troops were wounded, one of whom later died, a spokesman for the International Security Assistance Force (ISAF) said in Kabul.
An interior ministry spokesman in the capital added, "The suicide bomber has died, seven civilians have been wounded, two civilian children have been martyred."
The attack struck a military convoy that had been leaving a police station, the Ministry of Defence in London said.
ISAF could not say what had caused the explosion. One Afghan official told AFP it was a car bomb and another said the attacker had strapped explosives to his body.
The second suicide attack was near the south-eastern city of Khost and hit a police vehicle.
"One policeman was martyred and five were wounded in the suicide blast today," provincial criminal investigation director Mohammad Yaqoob told AFP.
The attacker was blown to pieces, he said.
There were 91 nation-wide this year, according to ISAF statistics up until Wednesday. More than two-thirds were by car bomb, spokesman Major Luke Knittig said.
The attacks killed 155 civilians, 40 members of the Afghan security forces and six government officials, he said. They had also claimed the lives of 14 foreign troops.
The extremists have this year mounted mass formation attacks on security forces but suffered heavy defeats. Military officials say this has led them to rely on suicide and roadside bombings.
They have "reverted to the weapons of the weaker party -- improvised explosive devices, suicide bombs, mines and the occasional ambush," the ISAF commander, British General David Richards, said this week.
Nato Secretary General Jaap de Hoop Scheffer said suicide bombers would not defeat the military alliance's efforts to ensure democracy prevails in Afghanistan.
"It does bring home that the Taliban and the other spoilers of the process of nation-building and democracy in Afghanistan are having to go with these kinds of horrible tactics -- improvised explosive devices, suicide bombers and so on -- because they know they can't beat Nato in other ways," he said in an interview with the BBC.
"I can assure you they will not beat Nato -- neither the UK nor other forces -- by employing these tactics," he said.
Reacting to the Lashkar Gah blast, British Prime Minister Tony Blair's official spokesman said: "Despite today's attack, we are making real progress in Afghanistan."

Copyright AFP (Agence France-Presse), 2006