Ms Thornberry is a committed Remainer who said she is “never going to be able to do anything other than campaign to remain” in any fresh referendum on Brexit.
But she said it was not “democratic” to try to overturn the result of the 2016 EU referendum without consulting voters again.
Liberal Democrats have enjoyed a surge in the polls – pulling ahead of Labour in some surveys – since Ms Swinson announced that the party will go into a general election on a policy of revoking the Article 50 letter informing the EU of Britain’s intention to quit.
Speaking to The House magazine, Ms Thornberry said: “The Lib Dems have gotten kind of Taliban, haven’t they?
“They’ve said they’re just going to revoke, there’s not going to be another referendum. I don’t think it’s very democratic to seek to overturn a referendum without asking the people first. I really think the only democratic way to get through this and to break the logjam is to go back to the people and trust their good sense.”
Ms Swinson responded: “Comparing a UK political party to the Taliban is ludicrous. Emily is the shadow foreign secretary, and should use language that reflects the importance of that role.”
And Lib Dem foreign affairs spokesperson Chuka Umunna said Ms Thornberry should “withdraw her inappropriate remarks”.
Mr Umunna said: “Language counts – comparing the Lib Dems to a murderous organisation is no laughing matter. It is also grossly insulting to over 23,000 of her constituents who signed the parliamentary petition for Article 50 to be revoked.”
But former leader Tim Farron adopted a more humorous approach – while also taking the opportunity to have a swipe at Jeremy Corbyn’s past meetings with representatives of Hezbollah and Hamas – tweeting: “Come on Emily, if we really were like a Middle East terrorist group, don’t you think Jeremy would’ve invited us to a conference fringe meeting before now?”
Ms Thornberry clashed with Mr Corbyn after Labour’s poor showing in the European elections, when she suggested the party should be committed to campaigning for Remain in any referendum. In an apparent act of revenge, she was passed over for the stand-in slot when the leader was absent for prime minister’s questions.
But she played down the snub, telling The House: “I’m pretty confident I’m doing it in the future. It was a decision for Jeremy and Loto [leader of the opposition’s office] to decide, it wasn’t for me.”
And she played down the significance of Labour deputy leader Tom Watson’s call for a second referendum before a general election, saying: “It’s just how he is, isn’t it? I haven’t seen him for a while ... But he’s deputy leader and he can say what he wants.”
Ms Thornberry recently got into difficulties on TV trying to explain Labour’s position on Brexit.
But she defended the position, saying: “We are now wedded to having a second referendum because so much has changed since three years ago. The question then is what will the choice be. We don’t want to put these lousy Tory choices of no deal or Theresa May’s deal to the public. We want there to be two good choices.
“I would say ‘anything other than leaving the European Union’ is not a good choice but it would be second best. We need to have a choice that will look after jobs and the economy as best we can, which means being in the customs union and being close to the single market.
“We’ve said we need, before we do finally leave, to have it confirmed with the public; if they do want to leave, this is a way that makes sense, or we remain. It’s important that we’re clear about that, but I’m never going to be able to do anything other than campaign to remain because I think we should be in the EU.”
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