Volodymyr Zelensky has met King Charles at Buckingham Palace, The Telegraph reports.
Speaking to Parliament earlier, the Ukrainian President again urged his allies to send him warplanes.
"Two years ago, I left Parliament thanking you for the delicious English tea. Today I will leave Parliament thanking all of you in advance for powerful English planes," said Volodymyr Zelensky in an address to MPs.
The surprise trip to Britain is the first time Mr Zelensky has visited the country since the start of Russia's invasion and only his second foreign trip in wartime.
It has also been announced that Mr Zelensky will meet Emmanuel Macron and Olaf Scholz at the Elysée palace in Paris this evening.
Zelensky has urged the UK to provide his country with fighter jets as he addressed Parliament during his first UK visit since Russia's military operation in Ukraine, BBC reports.
In an impassioned plea, he likened combat aircraft to "wings for freedom".
His call comes as the UK announced it will begin training Ukrainian forces to fly Nato-standard fighter jets.
President Zelensky concluded his speech with the hope that he would soon be thanking the UK for providing planes.
Later, Downing Street said that Mr Sunak has asked the defence secretary to investigate what jets the UK could potentially give to Ukraine, but emphasised it was "a long-term solution".
Addressing a huge crowd of MPs and peers in the historic setting of Westminster Hall, President Zelensky said: "Freedom will win - we know Russia will lose," adding the UK was with his country on a march to "the most important victory of our lifetime".
Thanking the UK for its "grit", he said the country, through its support of Ukraine, had not compromised the "spirit and ideals of these great islands".
He also singled out Boris Johnson for praise saying the former prime minister had united others "when it seemed impossible".
During his speech, which was met throughout with applause, the Ukrainian leader gave the House of Commons Speaker Sir Lindsay Hoyle the helmet of a Ukrainian pilot.
The writing on the helmet reads: "We have freedom, give us wings to protect it."
Reflecting on his last visit to the UK, he recalled thanking his hosts "for delicious English tea".
"I will be leaving Parliament today, thanking you all in advance for powerful English planes."
Mr Johnson echoed his calls in a statement saying: "It is time to give the Ukrainians the extra equipment they need to defeat Putin and to restore peace to Ukraine. That means longer range missiles and artillery, it means more tanks, it means planes."
BBC defence correspondent Jonathan Beale says that while the president gave an impassioned plea for Britain to give Ukraine fast jets, it still doesn't look likely that he'll get them, at least for now.
He says that it is still possible that a few Western nations could provide a small number of modern fighter jets to Ukraine at some time in the future, and that while Kyiv has made clear it would like US made F-16s, which are operated by a number of Nato countries, so far US President Joe Biden has said no.
