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Sir Keir Starmer has pledged to rip up Boris Johnson's "botched" Brexit deal after Labour's election win.
The Prime Minister, who backed Remain and a second referendum, said he wants closer ties with Brussels including on trade and security.
Speaking to reporters in Edinburgh yesterday, Sir Keir said: "We intend to improve our relationship with the EU and that means closer trading ties with the EU, it means closer ties in relation to research and development and closer ties in relation to defence and security.
"Obviously, there are many discussions to be had and negotiations to be had.
"But I do think that we can get a much better deal than the botched deal that Boris Johnson saddled the UK with."
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He added that it depends on "respectful relationships, talking to leaders across the EU and of course that work has already begun".
But former chief Brexit negotiator Lord Frost warned Labour cannot be trusted “at all” with Brexit.
He told Talk: “We can’t trust them at all. As you say, it’s obvious they want to rejoin, it’s only the perception that they can’t get too far away from their own Leave-voting base in large parts of the country that’s constraining them.
"Obviously they’ll want to do that and at the moment they’re at the stage of going around Europe, picking up positive vibes, trying to shape the debate.
“What I don’t think they understand is that if they want to get anything out of the Europeans, they’ve got to give something, and that means subordination to EU law, EU court, being part of the EU foreign policy apparatus again.
"I don’t know whether they’re up for that. They certainly should not be up for it because I think it would be deeply unpopular in the country.”
The Labour leader has previously insisted he would not seek to rejoin the single market or customs union.
It comes as Foreign Secretary David Lammy travelling to Europe over the weekend for talks with key players.
Writing in The Local Europe ahead of his trip, Mr Lammy said: "If we are to fulfil our ambitions for a reset, we must also improve Britain's relationship with the European Union."