The UK and Russia are examining the scope for a thaw in relations, including the possibility of a meeting between the Russian president, Vladimir Putin, and Theresa May at the G20 leaders’ summit in Japan at the end of this month.

If a meeting were to go ahead it would be the first encounter at this level since the poisoning in Salisbury of Sergei Skripal and his daughter in March last year – an episode that led to 23 Russian diplomats being expelled by the UK followed by the expulsion of a similar number of British diplomats from Russia.

The loss of the quality of the expelled British diplomats has severely damaged Britain’s capacity to analyse Russia from inside the country. Moscow also closed the British Council offices and the UK’s diplomatic outpost in St Petersburg.

No meeting between the two leaders would go ahead unless both sides felt certain it would be productive, and a common agenda is achievable. There is also a question of whether Putin would prefer to try to turn a new page with the UK with a new prime minister.

Boris Johnson, the Conservative leadership frontrunner, was sharply critical of Russia’s actions in Syria as foreign secretary, but before the poisoning had travelled to Moscow in December 2017 to meet the long-serving Russian foreign minister, Sergei Lavrov.

The G20 summit, in Osaka on 28-29 June, is likely to be May’s last international outing as prime minister. Putin briefly approached May at the last G20 in Argentina in November.

It is thought to be unrealistic to expect Russia to accept responsibility for the Skripal episode, or allow the two GRU agents to be extradited for trial in the UK.

The Foreign Office, and intelligence agencies, would have to judge whether some kind of acknowledgement that such episodes should not happen, or ever be repeated, the maximum likely to be offered, is sufficient for relations to be taken out of the deep freeze. Britain would need certainty that Russia had drawn the right conclusions from the episode.

Britain remains certain that the Russian state was responsible for the poisoning based on the information provided by Porton Down, the government’s chemical weapons research centre.

Two named Russian agents were identified by the UK government inquiry as travelling to Salisbury at the time of the poisoning, and the pair then attempted on TV to explain their visit simply as driven as tourists’ interest in the cathedral city. The inept explanation was seen as laughable inside Russia, and was thought to have embarrassed Putin.

May said the operation has been conducted by GRU intelligence agents and would almost certainly have been approved outside the GRU at a senior level of the Russian state.

Nevertheless, the UK side has been intrigued by recent public comments from Putin distancing the Russian political class from the actions of the spy agency. “When all’s said and done we need to turn this page connected with spies and assassination attempts,” Putin said recently on the sidelines of an economic forum in St Petersburg. He described Skripal, a former colonel in Russian military intelligence who betrayed dozens of Russian agents to MI6, as London’s spy.

“He’s your agent not ours. That means you spied against us and it’s hard for me to say what happened with him subsequently. We need to forget about all this in the final analysis,” said. According to Putin, “global issues related to common economic, social and security interests are more important than the games played by intelligence agencies”, he said.

The Russian president also mentioned his recent meeting with members of the British community, describing it as “very good”.

“We have $22bn-worth of British investment. These people want to feel secure. They would a positive trend in relations to emerge. We treat them as friends, whose interests must be protected regardless of the current political situation,” he said.

Christian Turner, Britain’s deputy national security adviser, went to Moscow this month to meet Russian ministers and officials. A level of co-operation is needed between countries intelligence agencies so that signals, such as troop movements, are not misread.