Tributes have been paid to Lt Col Thorneloe and Trooper Hammond
The defence secretary has paid tribute to two soldiers killed in Afghanistan, including the highest ranking officer killed since the Falklands War.
Bob Ainsworth said Lt Col Rupert Thorneloe, of the 1st Battalion Welsh Guards, was a "fine officer who had led his men with energy and pride".
Trooper Joshua Hammond, 18, from Plymouth, died in the same explosion in Helmand province on Wednesday.
It brings the number of British deaths in Afghanistan since 2001 to 171.
Six other soldiers were injured in the blast.
Mr Ainsworth said he knew Col Thorneloe, who he described as "a man of incisive thought, enormous professionalism and the greatest decency".
"As his own thorough and thoughtful tributes to those who fell before him show, he led his men with energy, care, and pride - and he died leading his men," he said.
"I cannot imagine a finer officer to have had in the front rank of the British Army, and his loss is all the harder."
Lt Colonel Thorneloe spoke to Huw Edwards in June, during coverage of Trooping the Colour
News of the latest fatalities came on the same day as the US army announced it had launched a major offensive against the Taliban.
Last week, UK troops launched their own push to drive the Taliban out of strongholds in and around Babaji, north of Lashkar Gah, in Helmand.
Col Thorneloe, who was commanding officer of the 1st Battalion, and Trooper Hammond, from the 2nd Royal Tank Regiment, died near Lashkar Gah when an improvised explosive device was detonated under their Viking armoured vehicle.
They had been part of a resupply convoy heading towards troops engaged in hostile territory.
Caroline Wyatt, BBC defence correspondent
These deaths will have a devastating impact for those who knew the two soldiers.
The loss of a commanding officer will be deeply felt by all in the Welsh Guards. But no less keenly felt will be the loss of Trooper Joshua Hammond.
There is an impact on morale too. Talking to soldiers in Helmand last Saturday, they said the way they got through the loss of their comrades was to band together, talk about it - and then get on with the job in hand.
Improvised Explosive Devices are probably the greatest threat to UK troops in Helmand Province even though more are being detected before they go off.
Gen Sir Richard Dannatt, Chief of the General Staff, said Col Thorneloe was "an outstanding commanding officer".
"His courageous, thoughtful stewardship of 1st Battalion Welsh Guards since October last year has seen them superbly prepared for the demands of Afghanistan, both in terms of their professional capability and their unbreakable spirit as a team," he said.
"At the leading edge of his generation, his loss will be felt deeply not only by his family but also by his soldiers and others, who like me, had the privilege to serve with him."
Col Thorneloe, who was from Kirtlington, near Oxford, and 1st Battalion were based at Lille Barracks, Aldershot, Hampshire, before deploying to Afghanistan, the MoD said.
He leaves his wife, Sally, and their two daughters, Hannah and Sophie.
His wife said: "Rupert was my very best friend and his death is a devastating blow.
"Rupert loved the Army. He was a born soldier - an inspiration."
She said her husband "felt privileged" to command his battalion, adding that he "led from the front and would not have had it any other way".
Regimental Lieutenant Colonel of the Welsh Guards Sandy Malcolm said he inspired "confidence, trust and huge respect".
"He was the consummate professional, charismatic, possessed an intellect that was as sharp as you can get, able to absorb issues large and small, and he was utterly charming," Lt Col Malcolm said.
The Viking was introduced into Afghanistan three years ago.
It was initially designed to defend against small arms fire and rocket-propelled grenades and therefore most of the armour was on the top of the vehicle.
Although the Viking is designed not to trigger anti-tank mines, it is still vulnerable to Improvised Explosive Devices (IEDs) because of the shape of the hull and a lack of substantial under-body armour
Last year the Ministry of Defence admitted it had reached the limit of how much it could be armoured following a series of deaths involving Taliban IEDs.
Vikings are due to be replaced for operations in Afghanistan by other, more heavily armoured, vehicles.
Trooper Hammond enlisted in the Army aged just 16 and died a week before his 19th birthday. He was engaged to be married.
In a statement, his family said: "Joshua was a tremendous son. He was proud to be a soldier and died doing a job he loved.
"We are devastated by the loss of Joshua, who was a loving son. We are proud of the fact that Joshua was prepared to do his duty, helping the people of Afghanistan."
Lt Col Marcus Simson, Commanding Officer 2nd Royal Tank Regiment, said that after only a month in theatre Trooper Hammond had already "proved himself to be a superb soldier".
"Fit, courageous and robust, he was the first to volunteer, the first to muck in and the first to offer help to others. But he was so much more than that," he said.
"For he was at the heart of everything that was going on. He was full of laughter, was always ready to listen and he cared deeply about his mates."
Col Thorneloe is the highest ranking officer in the British armed forces to die in Afghanistan.
He is also the most senior soldier to have been killed in action since Lt Col Herbert 'H' Jones in 1982.
Col Jones was posthumously awarded the Victoria Cross for his actions as commanding officer of 2nd Battalion, the Parachute Regiment, during the Battle for Goose Green during the Falklands conflict.
Brigadier Miles Wade pays tribute to Lt Col Rupert Thorneloe and Trooper Joshua Hammond
A Clarence House spokesman said the Prince of Wales, who is Colonel of the Welsh Guards, was "deeply saddened" by Col Thorneloe's death.
It is understood Prince Charles knew him well and his spokesman said he would be writing privately to both his family and his regiment.
In an interview with the BBC in February, shortly before deployment to Afghanistan, Col Thorneloe said he expected the mission to be "extraordinarily demanding".
"I think we view this as the most challenging mission that we as a battalion will face since the Falklands in 1982."
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