He will also urge UN members to come together to support equitable access to vaccines, warning that new virus variants will take hold in places where people have not been vaccinated, potentially threatening the rest of the world with new waves.
Mexico is also expected to raise concerns about unequal access to vaccines globally. Britain says it has provided 548 million pounds ($762 million) to help developing countries through the sharing initiative COVAX.
The British push for vaccination ceasefires could be a first key test of co-operation at the United Nations between China and the new administration of US President Joe Biden.
Long-simmering tensions between China and former US President Donald Trump's administration hit boiling point at the United Nations over the pandemic, highlighting Beijing's bid for greater multilateral influence in a challenge to Washington's traditional leadership.
Racked by bickering between China and the United States, the 15-member UN Security Council took more than three months last year to endorse a call by Secretary-General Antonio Guterres for a global pandemic ceasefire.
The Trump administration accused Beijing of a lack of transparency that it says worsened the Covid-19 outbreak. China denied those assertions.