Defence Secretary Bob Ainsworth, who is in Afghanistan, said it was vital to the UK's national security, while Army chief Gen Sir David Richards said the death had hardened "our determination to succeed".
Sir David also urged the public not to judge the campaign by casualties alone.
The US, the UK and other Nato countries have announced a surge in troop numbers, but America stressed it would begin to withdraw its military by 2011.
Afghan President Hamid Karzai warned it would take 15 years before Afghanistan was able to pay for the costs of maintaining its own security forces.
British troops arrived in Afghanistan in 2001 as part of a US-led invasion following the 9/11 attacks.
The total number of UK troops killed since the start of operations in 2001 has now reached 237.
'Full of resolve'
Maj Christopher Davies, commanding officer of C (Essex) Company, said L/Cpl Drane was "a thoroughbred soldier with huge potential".
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