The issue left the two leaders at odds as they agreed a 10-year trade co-operation deal and expressed the need to push common concerns in the EU — even though Britain refused to join closer fiscal union.
Mr Cameron drew Irish anger by appointing lawyer Desmond de Silva to consider evidence in the Finucane case — in apparent contradiction of a 2001 agreement to probe crimes involving state collusion.
Mr Finucane’s family have been granted a judicial review of the decision.
The Taoiseach insisted he would still press for a full review, adding: “I have a difference of opinion here with the prime minister.”
Mr Cameron dug in on the emotive issue, saying: “It’s not the nature of the review that matters — what matters is getting to the truth”.
“I don’t think it’s necessary for us to have a lengthy, judge-led, judicial review, with all the problems and costs and time that takes.”
However, the British leader heralded a new mood of positivity in relations between the two nations.
“Think of previous occasions with prime ministers and Taoisigh would have stood in this room or in Dublin, we would have been talking about political processes, parades, policing.
“Instead of that, there is another ‘p’ which is an entirely positive agenda between Ireland. It is about two countries which are friends and neighbours,” he said.
Mr Cameron said the two governments were united in a bid to defeat what he called the North’s “remaining terrorists”. Mr Kenny welcomed the agreement signed between the two countries.
“It covers a very broad spectrum of reality — recognising that the relationship between Ireland and Britain is now at an unprecedentedly high level of co-operation and interaction in trade and business, which is to the benefit of both,” he said.
The Taoiseach also spoke at the launch of the British-Irish Chambers of Commerce, which so far has attracted 150 companies as trade between the two countries continues to hold strong at €1bn a week.