Last week Britain became the first country to start supplying Ukraine with long-range cruise missiles, which will allow its forces to hit Russian troops and supply dumps deep behind the front lines.
Zelenskiy visited Berlin, Rome and Paris over the weekend to meet with European leaders as he seeks to drum up further military and financial support for Ukraine.
The British government said Zelenskiy had arrived in Britain and would meet Sunak at his Chequers country residence.
After the United States, Britain has been one of the largest suppliers of military aid to Ukraine, contributing 2.3 billion pounds ($2.9 billion) worth of support last year and pledging a similar amount for 2023.
In January, Britain said it would send 14 of its battle tanks to Ukraine, a pledge that was followed by other nations including the United States and Germany.