The Ukrainian president received an unprecedented honour guard on his arrival at No 10, made up of troops from the Irish Guards, amid what the Prime Minister described as “dark and difficult days” for his country.
Mr Burnham told Mr Zelensky: “You have seen the solidarity and the support you have got from everybody here in Britain.
“We are behind you and that will not change.”
Prime Minister Andy Burnham welcomes President of Ukraine Volodymyr Zelensky (Joran Pettitt/PA)
PA Wire
In return, Mr Zelensky said he was “thankful” for the support, and “very proud” that the British people had proved “one of the strongest partners in our history”.
The meeting comes during a period of strained relations between Ukraine and the United States after Donald 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”.
Recent days have also seen the US president suggesting Ukraine needs a new leader and claiming Russian leader Vladimir Putin wants a peace deal more than the government in Kyiv.
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.
Speaking in the Commons ahead of his meeting with Mr Zelensky, the Prime Minister said he would seek to restore Donald 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, as 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.”
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.
The accelerated support will see faster deliveries of British lightweight multi-role missiles to Ukraine, which have proved effective against Russian jet-powered drones.
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.”