The two leaders are discussing Brexit, Northern Ireland and the economy
Taoiseach Leo Varadkar has arrived at Downing Street in London for his first foreign trip as Taoiseach.
He is meeting the British Prime Minister Theresa May.
Speaking in advance of his visit to London, Mr Varadkar said: "I am looking forward to travelling to Downing Street today to meet the British Prime Minister, Theresa May.
"I want to renew the close bond and strong relations that exist between Ireland and the United Kingdom.
"Among other things, we will discuss Northern Ireland and the need to re-establish devolved government, and Brexit, focusing on how we can avoid any adverse impact on the rights and freedoms of our citizens, on trade and the economy."
Mr Varadkar and Mrs May have previously spoken by phone following his election as Taoiseach last week.
Mrs May's Conservative Party is still in talks with Northern Ireland's Democratic Unionist Party (DUP) on confirming its support for forming her second government.
It comes on the day the UK begins formal negotiations to leave the European Union.
The British Brexit Secretary David Davis and the EU's chief negotiator Michel Barnier will hold talks in Brussels.
Additional reporting: Gavan Reilly