The Russian president, in London to watch Olympic judo, talks world affairs, human rights and trade with the prime minister

David Cameron sought to find common ground with Vladimir Putin by highlighting their agreement over the need for a stable Syria following talks in Downing Street with the Russian President earlier today.

The prime minister issued a brief statement to cameras after the latest round of Olympic Games-focused diplomacy saw him welcome Putin amid growing tensions in Syria. The meeting happened after the collapse of the peace plan proposed by the former UN secretary general Kofi Annan who, it emerged later in the afternoon, has quit as the UN-Arab League envoy to Syria.

Britain and Russia are both permanent members of the UN security council, and the Russians, often with Chinese backing, have steadfastly opposed any form of UN resolution that could be seen to be supporting military intervention – or even military-backed humanitarian corridors.

At least three resolutions have been blocked by the Russians, and the British in turn were instrumental in preventing a Russian-originated arms shipment from reaching Syria.

As Putin visited Britain for the first time in seven years, the two leaders discussed the conflict, as well as bilateral trade and the Olympics during a meeting that lasted 40 minutes.

On Syria, Cameron pointed to differences in the British and Russian approaches, but said both were agreed on the need for an end to the conflict. "We both want to see … a stable Syria. We will continue to discuss with our foreign ministers how we can take this forward," said Cameron.

The Russian president made no direct reference to his country's stance on its long-standing ally, Damascus, but said that there were areas where Russia and Britain see eye-to-eye. "We agreed to continue working to find a viable solution," said the president.

The two leaders met amid ongoing tensions between their two countries over espionage, human rights, trade deals and the presence of a community of outspoken Russian political exiles in Britain.

The UK and Russia are still at odds over the 2006 death Alexander Litvinenko, the Kremlin critic killed by radiation poisoning in London, whose widow lives in Britain.

Putin's arrival also coincided with growing criticism over the case of three female members of the punk band, Pussy Riot, facing trial after staging a performance in a Moscow cathedral calling on the Virgin Mary to remove Putin from power.

Before the talks, leading musicians called for the release of the band members, who face up to seven years behind bars. Pete Townshend, Jarvis Cocker and Neil Tennant were among those who added their names to a letter in the Times, defending the band members' right to legitimate protest. Maria Alekhina, Ekaterina Samutsevich and Nadezhda Tolokonnikova, have been named prisoners of conscience by Amnesty International.

Earlier in the day, John Dalhuisen, Amnesty's Europe and Central Asia director, had urged Cameron to raise their case with the Russian president. "During Mr Putin's time in high office, Russia has become increasingly intolerant of legitimate dissent, and the Pussy Riot trial is just the latest example of this. By putting a group of women in balaclavas on trial, Russia's own mask has slipped. David Cameron should politely – but firmly – tell it like it is on the Pussy Riot case: the trial is a disgrace and the charges should be dropped immediately," he said.

A Downing Street source confirmed that Cameron had raised the matter with Putin as part of his wider concerns about human rights in Russia, although the source said that Putin was not particularly responsive. Cameron said the talks had also focused on bilateral trade issues and hailed the steady growth in UK-Russia relations.

Putin lavished praise on the opening ceremony of the London 2012 Olympics, which he described as unforgettable. Speaking through a translator, he described Danny Boyle's show as "a wonderful feast presented by you to mankind".

Following their brief address to camera, the two leaders headed for the final stages of the London 2012 judo competition, a martial art in which the Russian president holds a black belt. Cameron joked: "I look forward to taking the president to the judo, but I note that we will be spectators and not participants."

The visit sparked criticism from Labour's Denis MacShane, who said it was shameful that Putin had been invited to Downing Street without having to face public questions about Russia's UN veto or "the dramatic worsening of human rights in Russia, symbolised by the photo of the Pussy Riot girl rockers peering through prison bars like an image from the Soviet gulag".

McShane said the Olympic Games should not be used to promote "British appeasement of Putin".

He said: "Initially we were told Putin would not come to the Olympic Games after the House of Commons passed a unanimous resolution calling for action against his state functionaries in connection with the death of Sergei Magnitsky. Clearly, the chance of being photographed with Russia judoka in London was too good to pass by. It is also clear that Putin obtained assurances he would not face news media or be put under pressure on his stepping up of repression inside Russia. The extra red carpet rolled out today for Putin by David Cameron in exchange for nothing that he can report to the British public shows British foreign policy is again relegating human rights and democracy-promotion."

Evgeny Lebedev, the owner and publisher of the Evening Standard and the Independent, hailed Putin's visit to Britain as a "very important step forward" for relations between Russia and the West. Lebedev, son of the billionaire businessman and former KGB agent Alexander, said Russia had been isolated "for way too long".

Lebedev told the Radio 4's World at One that Russia's isolation could be prevented by keeping his country at the discussion table.

"The feeling I get is the more Russia feels isolated, the more its government becomes defensive. It's a very good step forward for the Russia president to be in London. That said, I think, I'm in Moscow and there are a lot of problems at the moment: opposition members have been charged, what's happened with the rock band Pussy Riot is giving Russia a bad name. The Russian government should appreciate that, so that the country can be treated as equal with Western democracies."

Lebedev said if Russia is kept at the table, a resolution to the Syria problem could be found.

"I think it's very important that there is discussion, that Russia feels that it is part of that open and frank discussion between itself and its western partners, and I think there is a potential for resolution."

• The first Russian motherboard based on ARM-processor Baikal-M