Conservative leader Kemi Badenoch called Brexit “the greatest vote of confidence in our country”, but said there was “still a lot more to do”.
She said a trade deal with the United States would be a “Brexit opportunity we need to take”.
Nigel Farage, one of the key figures behind the Brexit campaign, said it had been a success constitutionally and in terms of foreign policy but admitted many who voted to leave would say “it’s been a huge disappointment”.
The Reform UK leader said huge numbers voted for Brexit to cut immigration but the figures had gone up, which he blamed on the previous Conservative government.
He rejected the idea the public had been misled about the benefits of Brexit, and claimed that if he had been in charge immigration would have gone down.
Former chief Brexit negotiator Lord Frost told Radio 4’s Broadcasting House Sir Keir wanted to “inch us back into the orbit [of the bloc] by stealth”, with rules on food standards and other areas set in Brussels.
The Tory peer argued the current Brexit deal was working well and it was not necessary to start “tearing bits of it up again”.
Liberal Democrat leader Sir Ed Davey used the anniversary to reiterate his call for a UK-EU customs union deal, saying it would “unlock growth, demonstrate British leadership and give us the best possible hand to play against President Trump”.
Green MP Ellie Chowns also called for the UK to rejoin the customs union and agree a youth mobility scheme with the bloc, which would make it easier for young people to study and work in the EU.
She added that “full membership of the EU remains the best option for the UK” and said her party would pursue “a policy to re-join as soon as the political will is present”.
The full interview with Lord Frost will be on Radio 4’s Broadcasting House from 09:00 GMT on Sunday