In an unusual front-page op-ed in the Sunday Times, Cameron says there is growing evidence that separatist rebels, backed by Russia, shot down the aircraft, killing 298 people.
"If this is the case then we must be clear what it means: this is a direct result of Russia destabilising a sovereign state, violating its territorial integrity, backing thuggish militias and training and arming them," Cameron wrote.
"If President Putin does not change his approach to Ukraine, then Europe and the West must fundamentally change our approach to Russia," he wrote
Views in London are hardening on Ukraine amid anger over access at the crash site. Images from the site have shown rebels picking through the wreckage and personal belongings of victims.
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Foreign Secretary Philip Hammond told the BBC that Putin could "snap his fingers" to allow a proper investigation.
"The eyes of the world are on Vladimir Putin and what we are seeing from the Russians is obfuscation and obstruction at the moment," Hammond said.
"In Europe we should not need to be reminded of the consequences of turning a blind eye when big countries bully smaller countries," he wrote. "We should not need reminding of the consequences of letting the doctrine of 'might is right' prevail.