The cross-party Trident Commission said the UK should retain and deploy a nuclear arsenal for reasons of national security and its responsibilities to Nato.
However it added that the country should show keen regard for the shared responsibility to work towards global nuclear disarmament.
It also said that relaxing continuous at sea deterrence (CASD), where one submarine is always at sea, could be considered, though it was divided over whether the country could take the step independently or with other nations.
The Government will decide whether to renew Trident in 2016.
The Conservatives are committed to a like-for-like replacement for the existing four-boat fleet, but the Liberal Democrats say they would only build three new submarines.
Alex Salmond's Scottish Government has made its opposition to nuclear weapons clear, and wants the Trident submarines to be moved out of Scotland in the event of a Yes vote in this year's independence referendum.
In its report, the Commission said: "If there is more than a negligible chance that the possession of nuclear weapons might play a decisive future role in the defence of the United Kingdom and its allies, in preventing nuclear blackmail, or in affecting the wider security context within which the UK sits, then they should be retained.
"The impact of the UK's falling victim to ongoing strategic blackmail or nuclear attack is so significant that, even if the chances appear slim today, there is sufficient uncertainty surrounding the prospect that it would be imprudent to abandon systems that have a high capacity to counter such threats."
It considered three credible possibilities where the deterrent effect of an independent British nuclear capability might become decisive.
These were the re-emergence of a nuclear threat from a state with an "aggressive posture", an existing or emerging nuclear state attaining global reach and entering into direct strategic competition with the UK, and the emergence of a future threat involving bio-weapons or comparable mass destruction technologies.
The report concluded that the Trident SSBN (ballistic missile submarines) system meets the criteria of "credibility, scale, survivability, reach and readiness".
The current plans to construct and deploy four replacement SSBN submarines with missiles and warheads over the period 2016 to 2062 will account for 9.4% of the defence budget, the report said.
However it said this should be weighed against the deterrent role of nuclear weapons.
It said: "Over the life of the project, it can be expected that capital, running and decommissioning costs associated with the nuclear weapons project account for roughly 9-10% of the overall defence budget, though into the 2020s we will experience a higher spend, and after that a smaller amount.
"However, we believe that cost must be of secondary importance to the judgement over whether forsaking the UK's nuclear deterrent capability could open the country to future strategic risk."
The Trident Commission was set up in 2011 by the British American Security Information Council.
Members include former Conservative defence secretary Sir Malcolm Rifkind, ex-Liberal Democrat leader Sir Menzies Campbell, former chief of the defence staff Lord Guthrie of Craigiebank and ex-Labour defence secretary Lord Browne.
Its report also called on the Ministry of Defence to consider what steps it could take to work towards multilateral disarmament.
It said: "Such steps might not only be further reductions in warheads or changes in posture and declaratory policy, but could also include further transparency and verification measures, treaty-based commitments to control and reduce stocks of fissile materials and their means of production, and refraining from certain forms of development or modernisation.
"This will require a more explicit articulation of the conditions necessary for the UK to have the confidence to take such steps, and of national and collaborative actions that could bring these about."
It acknowledged that the UK has adopted a "stance of greater transparency" since the end of the Cold War.