Speaking at the CBI conference in London, Mrs May said that her Brexit plan is the best for jobs across the country.
In her keynote speech, she said: “We are not talking about political theory, but the reality of people’s lives and livelihoods. Jobs depend on us getting this right.
“And what we have agreed unashamedly puts our future economic success, and the livelihoods of working families up and down this country, first.”
Mr Corbyn told delegates: “A good Brexit plan for this country is not just about what can we negotiate in Brussels, it must also include a radical programme of investment and real change across all of the regions of Britain and the nations that make up the UK.
“Brexit should be the catalyst to invest in our regions and infrastructure, bringing good jobs and real control to local communities and people. If the Prime Minister is unable to negotiate an agreement that can win a majority in Parliament and work for the whole country, Labour’s alternative plan can and I feel it must take its place.”
In a Q&A session, Brexit-supporting businessman Roger Kendrick challenged the Prime Minister over her plans, which he said would restrict the ability to strike trade deals with countries outside the EU.
Mrs May told him “the portrayal that you have given of what has been agreed is a little inaccurate” and added: “It makes sense for us to continue having a good trading relationship with the European Union... but also have the freedom, which we will have, to sign those trade deals around the rest of the world.”
Mrs May told delegates that the UK values the contribution that immigration has made to Britain’s society and economy over many years.
“In the future, outside the EU, immigration will continue to make a positive contribution to our national life,” she said.
“But the difference will be this: once we have left the EU, we will be fully in control of who comes here. It will no longer be the case that EU nationals, regardless of the skills or experience they have to offer, can jump the queue ahead of engineers from Sydney or software developers from Delhi.”
Mr Corbyn told delegates that Labour wants to reduce the country’s reliance on the South.
He said: “A future Labour government will develop a comprehensive industrial strategy to rebalance our economy, reduce our reliance on the financial centre in London and the South East and increase prosperity in every region and nation of the UK.”
He said that many people who voted Leave in 2016 did so as an “act of protest” in response to the economic and political backdrop following the financial crash.
“In towns and cities hollowed out by industrial decline and neglect, with boarded-up shops and closed youth centres, many people voted for Brexit as an act of protest against a political system that simply wasn’t delivering,” he said.
“At the root of this was Britain’s profoundly unbalanced economy, chronic under-investment and failed economic policy. That needs to change.”
Responding to Mr Corbyn’s speech, CBI director-general Carolyn Fairbairn said: “Firms have made an offer to Labour - to work with business in a new partnership to solve the issues facing the UK and build a truly competitive and fair country.
“From rigid employment rules to blunt public ownership, the Labour approach sounds more command and control than partnership. This is not the change that is needed.
“Labour and business do share an ambition to tackle inequality, but the way to achieve this is through collaboration based on the belief that enterprise is a force for good.”