President Michael D Higgins joined prime minister David Cameron for lunch on the second day of his state visit to Britain today.

At 10 Downing Street, Mr Cameron extended “an extremely warm welcome” to the President.

“It is really remarkable how Anglo-Irish relations have not only been transformed but I see them on a ever-increasing gradient,” Mr Cameron said.

“I am really excited by the things that we are now doing together, two countries and two governments.

"I am excited by some of the new projects that we are talking about. But we must, as you said last night and Her Majesty [Queen Elizabeth] said last night, keep on with the work of reconciliation, including in Northern Ireland. "

Mr Cameron said the visit built on the queen’s “excellent and remarkable visit” to Ireland three years ago.

"It is a real privilege to be prime minister of the United Kingdom at a time when Anglo-Irish relations are on such an up.

“I am determined to do what I can and I know that the Taoiseach is as well to do what we can to play our part in building this very special partnership between two countries that are now not just neighbours, but really good friends and deep friends.”

Replying, the President said he was “absolutely delighted to be here and to be making this historic visit”, saying that Anglo-Irish relations are enjoying “ a great deepening kind of co-operation that is very important. It is obviously there in trade and the economy.”

Mr Higgins is attending a banquet in the Guildhall in London this evening.

The President's itinerary opened this morning with an event to mark the contribution of Irish people to the National Health Service. He was also scheduled to meet the mayor of London Boris Johnson.

A private but nonetheless significant engagement took place at the start of the day when the Duke of York showed the president the colours of the six disbanded Irish regiments which have been preserved in Windsor since 1922.

Along the Grand Stairs of the castle, the queen’s home, Mr Higgins inspected 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 will be shown to the president.

The castle was the setting for a historic state banquet in Mr Higgins’s honour yesterday where the queen said that Britain and Ireland shall “no longer allow our past to ensnare our future”.

Northern Ireland Deputy First Minister Martin McGuinness stood and joined in a toast to the Queen, the Duke of Edinburgh and the people of the UK as an orchestra played God Save The Queen.

The event was made all the more significant due to the presence of Mr McGuinness - a move unthinkable only a decade ago.

Mr McGuinness said today he believed he had the “overwhelming support of the people of Ireland” when he joined in the toast to the queen.

Speaking on RTÉ Radio 1, Mr McGuinness said the queen has been willing to show “impressive leadership” in the area of conflict resolution.

He said he “went into Windsor Castle as an unapologetic Irish republican and I’m still an unapologetic Irish republican” but he said toasting the queen was “the proper thing to do”.

He added that he has been cast into a position of leadership and said he has tried to provide leadership in building the peace process.

“I believe I have the overwhelming support of the people of Ireland for what I did last night.”

This morning former chairman of the Conservative Party Norman Tebbit is quoted in newspapers as saying he he hoped a dissident republican group would shoot Mr McGuinness for attending the banquet at Windsor Castle and toasting the queen.

Mr Tebbit and his wife were injured in the 1984 Brighton bomb. He said: “There’s always the possibility that a member of the Real IRA will be so outraged by Mr McGuinness bowing to the Queen that they might shoot him in the back for it. We can but hope.”

Responding to the comments, Mr McGuinness acknowledged Mr Tebbit and his family had been “very badly hurt by the conflict”.

But he said the remarks were “not fitting for someone in the elected position that he has been in for some time”. He added that he didn’t intend to make an issue of it.

In his speech last night, 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.

Additional reporting: PA