With the US midterm elections looming, Mr Trump confirmed his decision last week, citing violations by the Russians, whom he accused of testing and deploying prohibited intermediate-range cruise missiles.
The treaty was signed in 1987 by then-President Ronald Reagan and USSR leader Mikhail Gorbachev.
But Paul Ingham, executive director of the British American Security Information Council (BASIC) fears Mr Turmp’s decision risks triggering a renewed nuclear arms race.
He said: “Gavin Williamson’s stance the UK stands ‘absolutely resolute’ with President Trump is premature and irresponsible.
“NATO has consistently urged both parties to uphold the Treaty and since President Trump’s decision the EU, Germany and France have all urged President Trump to reconsider.
Mr Ingham claimed Mr Trump’s decision showed a “reckless disregard” for arms control and multilateralism.
He added: “His move risks deepening a nuclear arms race between the world’s two nuclear superpowers.”
With the Strategic Arms Reduction Treaty, commonly known as New Start, due to expire in 2021, Mr Ingham warned the world be left without any mutually agreed limits on the US and Russian nuclear arsenals since 1972.
He said: “Rather than recklessly withdrawing, the United States should exhaust all diplomatic measures to uphold the Treaty.
“We are all affected by US-Russia arms control.
“If the INF Treaty falls, Europe would be at unique risks, sandwiched between a new nuclear arms race.”
He said without such treaties in place, the world was at risk of a repetition of the so-called Pershing Missile Crisis which resulted from the tension resulting from Operation Able Archer 83, a NATO military exercise in 1983 which some USSR generals thought was a prelude to a nuclear strike.
Mr Ingham described the misunderstanding as having brought the world “closer to nuclear annihilation than any point since the Cuban Missile Crisis“.
He said: “In the context of deepening tension and polarisation on nuclear issues globally, it is incumbent on the UK to defend arms control and work cooperatively with the US and Russia to reduce nuclear risks.
“To do otherwise would be a grave error.”
In a blog published on BASIC’s webiste, nuclear policy analyst Maxwell Downman added: “The conditions for withdrawal should not be whether the United States believes Russia is violating the Treaty and whether the United States is the only ‘constrained’ party.
“Rather the United States needs to consider the impact of leaving the Treaty for wider European security in diplomatic, security and normative terms.
“Diplomatically, the move undercuts US credibility.
“The United States should exhaust all diplomatic options to address compliance concerns before leaving the Treaty.
“Cutting and running, in the words of Jeffrey Lewis, allows Russia ‘to violate the treaty and Trump takes the blame’.
Mr Gorbachev himself lamented the US decision to pull out of the treaty earlier this week, branding it a “dire threaet to peace” in a column written for the New York Times.
He said: “I am being asked whether I feel bitter watching the demise of what I worked so hard to achieve.
“But this is not a personal matter. Much more is at stake.
“A new arms race has been announced.”