Former Ireland captain Brian O'Driscoll was part of the delegation which made a 30-minute pitch to officials in London.
The taoiseach was the only state leader to attend in person as Ireland, France and South Africa all presented their bids to stage the tournament.
Liam Neeson, Bono and Bob Geldof all featured in the Irish presentation as British Prime Minister publicly backed the bid by writing to World Cup organisers reaffirming their support.
The World Rugby will announce the host of the 2023 Rugby World Cup on 15 November 2017.
He said: "I have always encouraged the British government to be more specific about how they see the future relationship between Britain and Ireland and between the United Kingdom and the European Union".
"And I'm very grateful for the fact that she's done that".
The Ireland bid party at today's presentation in London. We've put a great bid together, it's a partnership between North and South, between IRFU and GAA, between our Communities, Business, Diaspora and Government.
The 2015 World Cup in England set records in terms of ticket sales, TV viewing figures and income but Japan, hosts of the first Asian World Cup in 2019, will make much less money.
"Jonah Lomu loves France, that's where they saw their daddy playing rugby", said ex-France flanker Sebastien Chabal.
Sports minister Laura Flessel said that hosting the event along with the already-secured 2024 Olympics would provide "synergies of organisation" and that despite recent bomb attacks in the country, security was an equal concern of all bidding countries.