On the issue of Brexit, the taoiseach the will use his first meeting with the prime minister to raise a series of concerns. He told gathered reporters that there was "a little thrill in it".
He said on the way to the building he was "reminded of that famous scene in Love Actually where Hugh Grant was dancing down the stairs".
Mr Varadkar has said he wants to renew the close bond and strong relations that exist between Ireland and the UK.
"London is a very important city for Irish people", he added. "When there is an attack on London, we in Ireland feel it is nearly an attack on us as well", Varadkar said.
Irish prime minister Leo Varadkar said he had been reassured by British prime minister Theresa May that her plan to form a government with support from a Northern Irish party would not destabilise power in the province.
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"What I think we need to do is to build a new deep and special partnership with the European Union", she said.
"Of course I can't give you the detail of how that is all going to work out now because the negotiations have only just begun, but we have a shared objective to minimise the disruption to trade both north and south and east and west".
"But it is my first visit overseas and I really want to thank the Prime Minister for facilitating it at very short notice".
Northern Ireland's political parties are reopening talks aimed at restoring devolution to the region.
He also said during the press conference that Arlene Foster and the DUP "have a different view on this matter", before saying that "there wasn't a meeting of the minds on this issue, but it's not one that I'm not going to continue to raise".
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