Britain has warned Vladimir Putin that the "world's eyes are on Russia" as David Cameron urged the EU to "reconsider its approach" to the country.
The new foreign secretary Philip Hammond has demanded the Russian president ensure his country meets obligations to the victims killed in the Ukraine plane disaster.
His comments come as pro-Russian separatists were accused of removing 38 bodies from the Malaysia Airlines crash scene and attempting to destroy evidence at the site.
David Cameron and his Dutch counterpart Mark Rutte have now called for the European Union to "reconsider its approach to Russia" in light of evidence that pro-Moscow separatists brought down flight MH17, Downing Street said.
The European Union has already imposed sanctions, including visa bans and travel freezes, against Russians involved in efforts to destabilise Ukraine, but the comments from Downing Street indicate that further action could be taken.
Hammond said Russia is not giving "enough support" and that it is increasingly likely that the cause of the "terrible accident" was a missile fired from separatists in Eastern Ukraine.
He said the UK's priority is now to ensure the victims are treated with dignity and respect as they are recovered from the crash scene.
"We're not getting enough support from the Russians, we're not seeing Russia using their influence effectively enough to get the separatists, who are in control of the site, to allow the access that we need," he said.
"This has brought the whole international community together.
"This is not about Russia and the West, this is about the whole community demanding that the proper access is made available to this site, the victims are properly recovered and evidence is secured.
"The world's eyes will be on Russia to see if she delivers on her obligations in the next couple of hours."
The bodies of passengers which have been strewn across the crash site of Malaysia Airlines flight MH17 for nearly 48 hours are finally being recovered by Ukraine authorities. But Ukraine has accused rebels of already tampering with victims and their luggage - removing 38 bodies from the scene.
Looters have reportedly robbed the bodies of victims of the passenger jet, including Newcastle United fan John Alder.
The Ukraine government has said "terrorists, with the help of Russia, are trying to destroy evidence of international crimes", adding it had obtained data which showed bodies had been taken to a morgue in Donetsk.
Until now, many of the dead passengers had been left uncovered, lying among the plane wreckage in an open field in the rebel-controlled area.
In a sensational attack against Vladimir Putin, a Ukraine official earlier published an image purporting to show a tiny corpse of an infant victim of MH17 lying in a field, accusing the Russian President of murdering the baby.
Senior government advisor Anton Gerashchenko posted the graphic picture on Facebook with a message to Putin saying: "This baby's death is on your conscience", before adding "Damn you for centuries!"
Hammond added that the Russian ambassador to the UK will be called to the Foreign Office so the Government's views can be made known to him.
He said it was clear the monitors at the crash site had not been given full access by the rebels, and some areas were not possible to get to at all.
Ukrainian rebels may have tampered with the crash site of the Malaysian airliner MH17, it was alleged yesterday, with black boxes removed from the crash site and sent to Moscow "for investigation."
Gunmen yesterday prevented monitors from the Organisation for Security and Cooperation in Europe (OSCE) from observing the crash site in the battle-torn region of Donetsk, the rights and security watchdog said.
Critically, they said they were unable to speak to anyone about the whereabouts of the jet's two black box voice and data recorders.
Separatists reportedly fired warning shots as the group of 30 officials approached, forcing them to leave after just 75 minutes.
Michael Bociurkiw, spokesman for the OSCE, told CNN: "It basically looks like the biggest crime scene in the world right now, guarded by a bunch of guys in uniform with heavy firepower who are quite inhospitable.
"And there didn't seem to be anyone really in control, for example. One of our top priorities was to find out what happened to the black boxes. No one was there to answer those questions."
Specialists from the UK's Air Accidents Investigation Branch are in Ukraine, joining a broader international effort to investigate the crash.
A police-led victim identification team is leaving for Ukraine early tomorrow and will be available to see the victims as soon as the site is open to them. The Metropolitan Police earlier said they had offered their assistance.
Mr Hammond said he believed the total number of British victims is 10, but that the Government cannot be "absolutely certain" that more Britons will not be identified during the investigation.
He said the Foreign Office had been in contact with the families of all the known UK victims.
He stressed that the Government's priority is to ensure that the identification of victims and their personal belongings, as well as their recovery from the site, is treated with the respect and dignity it deserves.
"We are demanding that the Russians use their influence to ensure that access is granted. That's the only way we can get to the truth and bring those accountable to justice."