Theresa May branded Jeremy Corbyn a "blast from the past" as she claimed she remains optimistic over Brexit.
The Prime Minister also urged the Labour leader to "get his own act together" over his party's position on Britain's withdrawal from the EU.
Mr Corbyn countered by labelling the Government's approach a "shambles" as Brexit dominated the pair's exchanges at Prime Minister's Questions.
Mr Corbyn urged Mrs May to clarify how the Irish border will operate post-Brexit and accused the Government of seeking to weaken workers' rights and environmental protections.
He added: "Isn't the truth this Government has no energy, no agreed plan and no strategy to deliver a good Brexit for Britain?"
Mrs May replied: "The party in this Commons that has no clue on Brexit is the Labour Party. Week in and week out (Mr Corbyn) comes to this House and talks down our country and is pessimistic about our future.
"Well, let me tell him - I'm optimistic about our future.
"I'm optimistic about the success we can make of Brexit. I'm optimistic about the well-paid jobs that will be created. I'm optimistic about the homes we will build.
"That's Conservatives building a Britain fit for the future - all he offers is a blast from the past."
In lively and shorter exchanges between the two leaders ahead of the Budget, Mr Corbyn included a reference to Sarah Clarke - the first female Black Rod in the House of Lords.
He said: "I'm really pleased it's a woman at last who has got that position."
Mrs May, in her reply to his opening question, prompted cheers among her MPs by joking: "I'm glad you have welcomed the new Lady Usher of the Black Rod - I hope it isn't going to take 650 years before the Labour Party has a female leader."
After being questioned about Brexit, Mrs May also insisted: "We're very happy to move to further detailed discussions of the customs and trade relationship we will have, not just between Northern Ireland and the Republic but between the United Kingdom and the European Union."
The PM later accused Mr Corbyn of borrowing questions from the Liberal Democrats.
Mr Corbyn raised warnings over the UK financial sector losing its current trading rights with Europe, adding: "It seems neither the EU negotiators nor the Government have any idea where this is going.
"Last week, (Brexit Secretary David Davis) said he would guarantee free movement for bankers post-Brexit.
"Are there any other groups to whom the Prime Minister believes freedom of movement should apply? Nurses? Doctors? Teachers? Scientists? Agricultural workers? Care workers? Who?"
Mrs May replied: "I'm very interested (Mr Corbyn) has found that his appearances at Prime Minister's Questions have been going so well he's had to borrow a question from the leader of the Liberal Democrats, which he asked me last week.
"Perhaps the Leader of the Opposition should pay a little more attention to what happens in Prime Minister's Questions."