"Britain stands with Ukraine, shoulder to shoulder, and our support remains unwavering," Burnham said in a statement.
"Russia should be in no doubt of our resolve, and we will not back down until we achieve a lasting and just peace for Ukraine," he added.
The two leaders met at a naval base, where they were received a briefing on UK-led training programmes designed to strengthen Ukraine's armed forces and improve their battlefield capabilities, according to Downing Street.
Burnham and Zelensky also met with more than 200 Ukrainian military personnel and sailors who have spent the past three weeks in Britain participating in Exercise Sea Breeze, a maritime security and mine-countermeasure exercise intended to prepare participants for future operations in the Black Sea, the Reuters news agency reported.
Since Russia launched its full-scale invasion in 2022, Britain's total support for Ukraine has reached GBP 25 billion (EUR 29.2 billion, USD 33.3 billion), including GBP 16 billion in military assistance and GBP 5.6 billion in non-military support, Burnham's office said.
Speaking alongside Zelensky, Burnham also announced that Britain would provide Ukraine with new domestically developed jamming technology to help protect its drones from Russian electronic warfare, Reuters reported.
Burnham's predecessor, Keir Starmer, visited Kyiv days before leaving office earlier this month, where he pledged EUR 300 million (USD 345 million) to help equip Ukraine with a squadron of 16 Swedish-made Gripen fighter jets, according to Reuters.
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Source: Reuters, TVN24