Dubbed "Jonah Lomu - Unstoppable in London" the dinners costs nearly $600 a head and are sold out.
Mr Key left Brussels early this morning after talks about a comprehensive free trade agreement with European Union leaders Donald Tusk and Jean-Claude Juncker.
He begins the official British leg of his overseas tour early tomorrow which includes a meeting with Home Secretary Teresa May, an audience with the Queen at Windsor Castle and a "jeans and jersey" informal dinner with British Prime Minister David Cameron and his family at his private home in Oxfordshire.
Mr Cameron is said to be doing the cooking, according to Mr Key.
On Mr Key's last meeting he was invited to the official retreat of British Prime Minister, Chequers.
And on his last encounter with the Queen, Mr Key and his family were guests for the weekend at Balmoral Castle in Scotland.
It will be Mr Key's fifth audience with the Queen in Britain.
Mr Key said that in his meeting with Teresa May he will be asking that New Zealand's strong historical links with Britain be taken into account in any future restrictions on foreigners to work there.
Mr Key's past audiences with the Queen in Britain:
• 25 November 2008 at Buckingham Palace
• 26 April 2011 at Windsor Castle
• 7 June 2012 at Buckingham Palace
• 22 September 2013 at Balmoral Castle
• 30 October 2015 at Windsor Castle