The Prime Minister hosted the Ukrainian president for talks in Downing Street on Wednesday amid what he described as “dark and difficult days” for the war-torn country.
Mr Zelensky received an unprecedented honour guard made up of troops from the Irish Guards on his arrival at No 10 and was told by Mr Burnham that Britain is “behind you and that will not change”.
In a readout of the meeting, a Downing Street spokesperson said: “The leaders began by reflecting on their call on Saturday, and Russia’s blatant indiscriminate attacks on civilians and energy infrastructure since President Trump called for an energy ceasefire.
“It was clear that Russia had no interest in peace, the leaders underlined.”
They discussed how Ukraine’s allies could step up support, with the Prime Minister pointing to faster deliveries of British lightweight multi-role missiles, which have proven effective against Russia’s barrage of jet-powered drones.
During his meeting with Mr Zelensky, he confirmed that the UK would accelerate the supply of crucial air defence missiles to Ukraine amid “heavy bombardment” from Russia.
Mr Zelensky received an unprecedented honour guard as he was welcomed to Downing Street (Hannah McKay/PA)
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Mr Burnham said the UK would continue in its “diplomatic efforts” to secure international supplies of defensive equipment and focus on developing new ways of supporting Kyiv on the battlefield, such as retrofitting British capability onto supplies gifted from other nations.
The meeting comes during a period of strained relations between Ukraine and the United States after Mr Trump eased sanctions on Russian diesel last week as high fuel prices in the US threatened to overshadow November’s mid-term elections.
The UK responded to news of the deal by pledging to “maintain pressure on Russia”.
In recent days, the US president has suggested Ukraine needs a new leader and claimed Russian leader Vladimir Putin wants a peace deal more than the government in Kyiv does.
Concerns have also been raised about intelligence sharing from the US, with Mr Zelensky saying Kyiv had received no warning about Russian missile strikes on Monday and Tuesday.
An honour guard welcomed Mr Zelensky to Downing Street (Jordan Pettitt/PA)
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Speaking in the Commons ahead of his meeting with Mr Zelensky, the Prime Minister said he would seek to restore Mr Trump’s support for Ukraine.
During Prime Minister’s Questions, Mr Burnham said he was being “careful” in his language after Mr Trump’s diesel deal with Russia, because he said he was “laying the ground” for a reconciliation.
He added: “I will listen to President Zelensky carefully, but he won’t be going away from Britain today empty-handed.”
Mr Burnham also said he had asked his ministers to examine other options for supporting Ukraine, telling Mr Zelensky they were “looking at all possible avenues”.
And he insisted that the Ukrainian president was “prepared to sit down and discuss” the energy ceasefire proposed by Mr Trump, but added: “Sadly, what we have seen from Russia is further attacks on critical national infrastructure in Ukraine.”
He said: “In these moments, Britain will continue to provide you with whatever support we can.”