The Ukrainian president is in Britain after visiting Paris, Berlin and Rome on a whistlestop European tour.
Britain pledged Ukraine hundreds more missiles and attack drones on Monday, following a meeting between the two countries' leaders.
“This is a crucial moment in Ukraine’s resistance to a terrible war of aggression they did not choose or provoke," said British Prime Minister Rishi Sunak.
"They need the sustained support of the international community to defend against the barrage of unrelenting and indiscriminate attacks that have been their daily reality for over a year.
“We must not let them down.”
Britain, a staunch ally of Kyiv, will give Ukraine “long-range attack drones" with a range of more than 200km. At the upcoming G7 meeting later this week, it will push allies to deliver more support, according to Downing Street.
The Ukrainian president was helicoptered to Chequers, the official country retreat of PM Sunak on Monday morning, thanking London for all its support so far.
The war is a matter of “security not only for Ukraine, it is important for all of Europe," said Volodymyr Zelenskyy, adding their meeting would cover “very important issues, urgent support for Ukraine”.
Sunak told Zelenskyy: “Your leadership, your country’s bravery and fortitude are an inspiration to us all.”
Last week, Britain announced it had sent Ukraine Storm Shadow cruise missiles, which can hit targets more than 250km away.
"The UK is leading the way when it comes to expanding our capabilities on the ground and in the air. This cooperation will continue today. I will meet my friend Rishi. We will conduct substantive negotiations face-to-face and in delegations.”
Kyiv has repeatedly asked for long-range military equipment, saying it is essential to beat back Russian forces. However, there have been concerns such deliveries could escalate the conflict, enabling Ukraine to strike deep inside Russia.
London hopes its military aid will help change the course of the war, sending country Challenger tanks and training 15,000 Ukrainian troops on British soil in the past.
Zelenskyy's visit to Britain - his second since invaded in February 2022 - is the latest stop in his European tour which has already taken in Paris, Berlin, Rome and the Vatican over the weekend.
He is seeking more aid as Ukraine prepares a long-anticipated spring offensive to retake territory seized by Russia.
Ukraine's leader held an unannounced meeting with French President Emmanuel Macron on Sunday, after trips to Germany and Italy, where he met those countries' leaders and Pope Francis.
As Zelenskyy visited European capitals, Russia stepped up attacks across Ukraine with drones and missiles over the weekend.