Mr Higgins had a private lunch and bilateral discussions with Mr Cameron at 10 Downing Street on Wednesday afternoon.The President of Ireland told the Prime Minister: "I'm absolutely delighted to be here making this historic visit."In every aspect of our relationship there is a great deepening of co-operation which is very important and I hope this visit will enable greater opportunities for the deepening of the peace process which of course will require our continued vigilance."I want to say thank you as well for the reception I've received."Michael D Higgins also met London Mayor Boris Johnson at City Hall where he attended a unique youth leadership function for children from both nations.Boris Johnson tweeted: "A joy to welcome Irish President Michael D. Higgins to City Hall. Discovered we share a love of Horace & Aeschylus."Mr Higgins said he had found it "inspiring and uplifting" to hear the thoughts and insights which had been put forward at the event on the challenges of the present and the path to a better future.He then met with Deputy Prime Minister Nick Clegg at Buckingham Palace before attending his final engagement of the day, a banquet at the Guildhall hosted by the Lord Mayor.Among the 700 guests were the Duke and Duchess of Gloucester, deputy First Minister Martin McGuinness, SDLP MP Mark Durkan and a host of famous faces.Michael D Higgins delivered a speech at the event. He said: "The intertwined histories of Ireland and Britain have indeed known great turbulence, but we meet at a time when the relationship between us has never been more friendly or respectful. The President and Sabina Higgins arriving at the Guildhall this evening #IrishStateVisitpic.twitter.com/RYSeipZH5e— IrishForeignMinistry (@dfatirl) April 9, 2014"The vibrancy of this relationship now irrigates every aspect of our societies. Tonight, it is perhaps appropriate to recall and emphasise the social, cultural and economic currents in that relationship, which flow so evenly and naturally now that we may underestimate their significance."Earlier, during Prime Minister's Questions, David Cameron praised Northern Ireland's politicians for the progress made on peace, making reference to deputy First Minister Martin McGuinness' attendance of the state banquet hosted by The Queen on Tuesday evening.He said: "Anyone who believes change isn't possible or politicians in NI can't rise to the challenge would have been very struck, as I was, to see Martin McGuinness around the table at Windsor Castle toasting the Queen last night at the banquet celebrating British/Irish relations."People have come a huge way and we need to continue with that vital work including the work to fight racism and sectarianism wherever it arises."Above all what we need is politicians in Northern Ireland to build a shared future to take down those peace walls, make sure the economy can grow and that there are opportunities for all in NI."The Irish President, who is making the country's first ever state visit to the UK this week, began day two of his four-day visit with the Duke of York showing him the colours of the six disbanded Irish regiments which have been preserved in Windsor since 1922.Along the Grand Stairs of The Queen's home, Mr Higgins viewed a piece of history in safekeeping for 92 years at the behest of King George V after 200,000 Irish men enlisted to fight for the Crown.The regimental flags of the Royal Irish Regiment, the Connaught Rangers, the Leinster Regiment, the Royal Munster Fusiliers, the Royal Dublin Fusiliers and cavalry unit the South Irish Horse were also put on display.It is a source of the greatest hope and confidence in the future to be in the presence of young people who have that remarkable ability to think about life in a way that is liberating, that is inclusive, and that has both the confidence and the moral courage to question the way things are and to set about making them better.Michael D HigginsOn Wednesday morning, Mr Higgins and his wife Sabina visited the University College London Hospital where they saw first-hand the hospital's work with older patients with dementia and the hyper acute stroke unit and met with past and present staff originally from Ireland.Day two also included a trip to the Royal Society where science partnerships were showcased.The president then attended a unique youth workshop at City Hall, titled Taking Charge of Change Together, where young people from both countries who are involved in Gaisce - The President's Award and The Duke of Edinburgh's Awards all took part.In a speech Mr Higgins said: "I know that many of our participants here today are from Northern Ireland, and that they are the first generation to grow up there as inheritors of a peace process founded on the cornerstones of equality and democratic partnership.""Not only did the Good Friday Agreement of 1998 provide a template for peace and reconciliation within NI, it also enabled a more dynamic and fruitful relationship between Ireland and Britain."On Tuesday evening, Windsor Castle was the setting for a historic state banquet in Mr Higgins's honour where the Queen said: "My visit to Ireland, and your visit this week, Mr President, show that we are walking together towards a brighter, more settled future."My family and my government will stand alongside you, Mr President, and your ministers, throughout the anniversaries of the war and of the events that led to the creation of the Irish Free State.The Queen"We will remember our past, but we shall no longer allow our past to ensnare our future. This is the greatest gift we can give to succeeding generations."The Queen also made reference to the peace process in Northern Ireland."Our two governments will continue to work together in Northern Ireland to support the First and Deputy First Minister and the Executive to advance the peace process and to establish a shared society based on mutual respect and equality of opportunity," she said.She ended her speech by asking guests - including famous faces such as Daniel Day-Lewis, Dame Judi Dench and Irish rugby hero Brian O'Driscoll - to rise and drink a toast to the president and his wife Sabina and "to the health and prosperity of the people of Ireland".In his own speech, Mr Higgins made reference to the Queen's historic visit to Ireland, saying: "Admirably, you chose not to shy away from the shadows of the past, recognising that they cannot be ignored when we consider the relationship between our islands."He said her "apt and considered words when you addressed some of the painful moments of our mutual history" were valued.In what was viewed as a major peace-building move, NI's deputy First Minister Martin McGuinness was in attendance at the banquet after accepting an invite from the Monarch.Following the speeches, the former IRA member turned Sinn Féin politician stood and joined a toast as the orchestra played God Save The Queen.