His comments come after UK Prime Minister Theresa May said on Monday that US tariffs on EU steel are “unjustified and deeply disappointing”.
May was speaking by phone with US President Donald Trump for the first time since the levies were imposed last week.
Downing Street said the 30-minute call was constructive and stressed the close national security relationship between the two countries.
May will not push for a UK exemption to the new US border tariffs of 25 per cent on EU imports of rolled steel and 10 per cent on aluminium as the UK will join the bloc’s push for European exemption.
The EU has been particularly vocal in criticising the tariffs and has threatened retaliatory action.
On Tuesday, Tannock also spoke out against the US tax and other recent measures taken by Trump, including withdrawing from the Iran nuclear deal.
He said, “In my 19 years an MEP I have never known transatlantic relations between the EU and the United States to be in such a fragile state.”
The British deputy added, “Clearly Trump no longer believes in the multilateral system between close allies which share the same democratic values to the same extent as previous US administrations.
“Indeed, some might go further to state that Trump is determined to reverse seven decades of an international rules-based order to make America more protectionist and the world into a series of big powers led by strongmen operating on a bilateral basis.
Trump seems also determined to weaken multilateral organisations starting with cutting US financial support to UN agencies and now aiming to paralyse the WTO by refusing to appoint judges to the appellate body dealing with international trade disputes.”
Tannock went on, “Clearly the US’s unilateral withdrawal from the Iranian JCPOA deal is a huge threat to the nuclear non-proliferation legal architecture and the EU are now trying desperately to salvage this in spite of the threat of US sanctions against EU companies doing business with Iran.
“The most recent further shock to EU-US relations was the announcement to impose high protectionist tariffs on EU steel and aluminium exports on the spurious grounds of ‘national security’ in spite of many of the countries affected being close Nato allies.”
Tannock, who sits on Parliament’s foreign affairs committee, said, “This would include, ironically, the UK which had pinned its hopes on the special relationship with the US coming to its rescue after Brexit.
“The UK will have to make some difficult choices but I believe that with the JCPOA, steel tariffs and the decision by US to withdraw from the Paris climate change accord, the UK is going to side with the rest of the EU rather than its traditional US ally under Trump.”