Thornberry, who leads the House of Commons foreign affairs select committee, said a broad deal resembling a 2015 agreement from which US President Donald Trump withdrew in his first term would likely be needed to resolve the nuclear impasse.
“Donald Trump egged on by Netanyahu decided to turn his back on it and he thought there were other ways that he could get what he wanted," she said.
"Clearly he hasn't, and there's been bombing in between and bombing with Israel and America. We need to get back into an agreement and I suspect we need to get back into something that's going to look very much like the JCPOA."
Her remarks are a rare critique of US policy toward Iran by a prominent member of the ruling party of a key US ally. US attacks on three Iranian nuclear sites capped off a 12-day war between Israel and Iran last month.
Trump said the attacks had "obliterated" Iran's nuclear program and has been ambivalent about the need for further talks.
European powers including Britain have mooted triggering renewed United Nations sanctions on Tehran if it does not return to negotiations on its nuclear program.
Iranian threats on UK soil
The UK Parliament’s Intelligence and Security Committee (ISC) last month warned that Iran poses one of the gravest state-based threats to British national security, on par with adversaries like Russia and China.
Asked whether Iran might be more dangerous following the war, Thornberry stressed the need for talks to defuse tensions.
"I think any country, if they feel isolated is likely to be more dangerous. That's the reason, one of the many reasons, why we want to be able to talk to Iran and bring them in," she said.
"We cannot accept it, and we have to make sure that we protect people. I've had people come to talk to me who personally feel threatened by the Iranian regime," she added. "We need to be able to live peacefully with one another and we need to be a center of free thought and an open discussion."
British interior minister Yvette Cooper said in May that Iran posed an "unacceptable threat" to domestic security after authorities charged three Iranian nationals under a national security law following a major counter-terrorism investigation.
The sharp statement came after the arrests of Iranian nationals on UK soil in terrorism-related cases.
In two separate operations on May 3, eight men including seven Iranians were arrested by the British counter-terrorism police.
Three of the Iranian nationals were later charged with offences under the National Security Act, accused of acting on behalf of Iran’s intelligence service and carried out surveillance targeting Iran International journalists.