By David Hughes and Richard Wheeler, PA
Sir Keir Starmer said work had already begun to build closer ties with the European Union following Labour's landslide election victory.
The prime minister said he wanted better trade and security relations with Brussels and pledged to tear up Boris Johnson's botched deal.
Foreign Secretary David Lammy has already travelled to Europe for talks with key players, promising that the UK would be a good neighbour after years of Brexit criminology.
Speaking to reporters in Edinburgh, Sir Keir said: “We intend to improve our relationship with the EU, which means closer trade links with the EU, closer research and development links and closer defence and security links.”
There are obviously a lot of discussions to be had and negotiations to be conducted.
But I think we can get a much better deal than the botched deal that Boris Johnson imposed on the UK.
He added that this depends on respectful relations, discussions with leaders across the EU and of course the work has already started.
Mr Lammy used his first overseas trip as Britain's top diplomat to impress on his German, Polish and Swedish counterparts that they had the opportunity to seize the opportunity for a reset and work even more closely together to tackle common challenges.
Mr Lammy identified support for Ukraine and climate change, as well as student holidays and exchanges, as areas where this can take place.
Separately, Business Secretary Jonathan Reynolds said restoring freedom of movement with the EU was not on the agenda as part of efforts to improve post-Brexit trade.
In an article published in The Local Europe, Mr Lammy said: “As the new UK Foreign Secretary, together with our Prime Minister Keir Starmer, this government will restore relations with Europe as a reliable partner, a secure ally and a good neighbour.”
Mr Lammy continued: “If we are to achieve our reset ambitions, we must also improve Britain’s relationship with the European Union.”
He said the government's proposal for an ambitious and far-reaching UK-EU security pact would seek to support closer cooperation between us.
He added: “Today, we all share a commitment to democracy, human rights and international law. The tragic experiences of our continents’ shared past have helped us understand how our common security and prosperity depend on these shared values.”
I believe that these values also form the basis for a closer partnership in the future. My visit this weekend is just the beginning. I look forward to seeing Britain reconnect with our European neighbours in the years to come.
Mr Lammy spoke to EU foreign policy chief Josep Borrell and the two men agreed to meet as soon as possible.
The Foreign Secretary could attend the September meeting of the EU Foreign Affairs Council even though the UK is no longer a member of the bloc.
Mr Borrell said the two men had a good conversation and discussed EU-UK foreign and security policy cooperation, recent developments in the Middle East and support for Ukraine.
On the Sunday morning show, Business Secretary Mr Reynolds said removing some of these trade barriers made sense when discussing future collaboration with the EU.
He told Sky News Sunday Morning With Trevor Phillips: “We talked about recognising each other's professional qualifications, again in an entirely reasonable and pragmatic way.”
If you work in the creative sector, you have really suffered from the restrictions on your travel within the European Union. These are practical things.
Asked about the free movement of people, Mr Reynolds said: “We are not open to the free movement of people, that is something that is part of membership of the European Union and, as I said, we will not revisit that.”
Irish Prime Minister Simon Harris said there was a willingness within the EU to talk to the new British government.
The Taoiseach told Sky News: I absolutely think there would be a fair hearing for any proposal from the UK Government or indeed the EU to address the practical issues in terms of a relationship that works.
Brexit has happened, the British have made this decision. But is it really possible to reach a veterinary agreement, to promote student mobility, to work more closely together on certain issues? I think so.