By Steve Holland and Gerhard Mey

LONDON/WINDSOR, England (Reuters) -U.S. President Joe Biden will look to deepen his relationships with Britain's King Charles and Prime Minster Rishi Sunak at separate meetings on Monday where climate change and Ukraine are expected to dominate the agenda.

Biden landed in London late on Sunday to kick off a three-nation trip including a NATO summit in Lithuania aimed at showing solidarity with Ukraine against Russia's invasion while not yet accepting Kyiv as a member of the alliance.

On Monday at Windsor Castle, the 80-year-old president and the 74-year-old king will discuss how to help boost private investment to combat climate change, a threat both leaders say is existential.

"The president has huge respect for the king's commitment on the climate issue in particular. He has been a clarion voice on this issue," White House national security adviser Jake Sullivan told reporters aboard Air Force One on Sunday.

Sullivan said Biden hopes to deepen his personal relationship with King Charles. He said the two leaders - who don't know each other well - had a phone conversation earlier this year that he described as "incredibly warm".

The king will receive Biden in the quadrangle of the castle, where a guard of honour will give a Royal Salute and the U.S. national anthem will be played, the king's office said.

Biden met the king's late mother, Queen Elizabeth, for tea at Windsor in 2021.

Earlier, the president will travel to 10 Downing Street on to hold a low-key meeting with Sunak, their fifth in as many months. Sullivan said the visit is more of a continuation of a long-running conversation than a formal meeting. It will mark Biden's first visit to Downing Street as president.

Sullivan said the two leaders would share notes before the NATO summit in Lithuania, which kicks off on Tuesday and will be dominated by the Ukraine crisis, which has brought members of the alliance closer.

Ahead of the trip, Biden urged caution for now on Ukraine's campaign to join NATO, saying the alliance could get drawn into the war with Russia due to NATO's mutual defense pact.

"I don't think there is unanimity in NATO about whether or not to bring Ukraine into the NATO family now, at this moment, in the middle of a war," Biden said in a CNN interview that aired Sunday.

Biden's trip comes a few days after he agreed to send U.S. cluster munitions to Ukraine.

Such munitions are banned by more than 100 countries, including the United Kingdom, due to their threat to civilian populations because they typically release large numbers of smaller bomblets that can kill indiscriminately over a wide area.

Russia, Ukraine and the United States have not signed on to the Convention on Cluster Munitions, which bans production, stockpiling, use and transfer of the weapons.

"I think you find Prime Minister Sunak and President Biden on the same page strategically on Ukraine, in lock step on the bigger picture on what we are trying to accomplish, and as united as ever," Sullivan said on Sunday.

Sunak, asked about cluster munitions on Saturday, said Britain was a signatory to the convention that discourages their use, and said it would keep doing its part to support Ukraine.

(Additional reporting by Gerhard Mey in Windsor and Jarrett Renshaw; editing by Leslie Adler and Mark Heinrich)