Boris Johnson has claimed Theresa May's Brexit speech outlined a "very attractive vision" of a strong Europe "buttressed and supported" by a strong UK.
The Foreign Secretary said the UK will be "able to do our own thing" by working with the EU on defence, security and to also deepen economic links, as he dismissed suggestions nothing will change until 2021.
Labour leader Jeremy Corbyn said the only advance was the Prime Minister listening to his party and realising the need for a transition period "on the same basic terms" to provide stability for businesses and workers.
Former Ukip leader Nigel Farage criticised Mrs May's vision, claiming Britain will leave the EU in "name only".
Theresa May's Brexit vision is that we Leave the EU in name only. All areas of integration we have currently will be rebadged.— Nigel Farage (@Nigel_Farage) September 22, 2017
Manfred Weber, leader of the centre-right European People's Party in the European Parliament and a key ally of German Chancellor Angela Merkel, said the UK position was still unclear and he is "even more concerned now".
In substance PM May is bringing no more clarity to London's positions. I am even more concerned now. #florencespeech— Manfred Weber (@ManfredWeber) September 22, 2017
Mr Johnson, when put to him that nothing will change until 2021, told reporters in Florence: "No, no, no, as the Prime Minister rightly said we are going to have a transition period and after that, of course, we are going to be taking back control of our borders, of our laws and of our destiny.
"I think what was so uplifting about this speech was it was positive, confident about what Britain can do, but also about our relations with the rest of the EU, and I think what it sets out is a very attractive vision of a strong Europe buttressed and supported by a strong UK.
"We're not going to be, as she made it very, very clear, in a relationship like Norway - receiving laws but not being able to change them or to vote on them.
"We're going to be able to do our own thing but also to work positively together on defence, on security and to build and to deepen that economic partnership."
Mr Corbyn accused Mrs May and her Conservative Cabinet colleagues of spending more time "negotiating with each other" than with the EU.
He said: "Fifteen months after the EU referendum the Government is still no clearer about what our long-term relationship with the EU will look like.
"The only advance seems to be that the Prime Minister has listened to Labour and faced up to the reality that Britain needs a transition on the same basic terms to provide stability for businesses and workers."
Mr Weber raised concerns, writing on Twitter: "In substance PM May is bringing no more clarity to London's positions. I am even more concerned now.
"The clock is ticking and time is running faster than the government believes in London."
Liberal Democrat leader Sir Vince Cable said Mrs May was admitting the UK will have to pay a "hefty Brexit bill" which amounts to several billions of pounds.
He said: "Both the Conservatives and Labour have now essentially converged on the same position, which is to kick the can down the road and simply delay the economic pain caused by an extreme Brexit."
Both Conservatives and Labour have converged on the same position, kick the can down the road and delay economic pain of an extreme Brexit— Vince Cable (@vincecable) September 22, 2017
The pro-Brexit Conservative former cabinet minister Owen Paterson expressed concern about the proposed two-year transition period.
"As long as we still have that transition period we are still bound in by European rules and we cannot get cracking on opening up markets around the world," he told BBC News.
He said that ministers should now start making preparations for the prospect that the UK will leave the EU without a trade deal.
"We just want simple, reciprocal free trade on a zero-tariff basis respecting each other's standards and regulations," he said.
"If they are not going to be serious about that, then I think we have to make them wake up to the fact we are not frightened of walking away."