The opposition will join forces with Tory Remain supporters and other parties to try to block Article 50 if the Prime Minister does not guarantee access to single market, the Labour leader told the Sunday Mirror.
Mr Corbyn suggested Mrs May, who has a slim Commons majority, would be forced into an early election if she fails to meet Labour demands, according to the newspaper.
But the PM issued a stern warning to MPs and peers who “regret the referendum result” that they “need to accept what the people decided” as she flew off to India for trade talks.
The Government is appealing a High Court ruling ordering the premier to seek MPs’ approval to trigger Article 50 and has insisted the deadline to begin Brexit by the end of March will be met.
Mr Corbyn said the UK must have continued access to the single market and there must be no watering down of workers’ rights before Labour will back the process.
He is also demanding protections for consumers and the environment and a promise that the cost over lost investment is covered by the Government.
He told the Sunday Mirror: “The court has thrown a big spanner in the works by saying Parliament must be consulted. We accept the result of the referendum.
“We are not challenging the referendum. We are not calling for a second referendum. We’re calling for market access for British industry to Europe.
“If the Government calls an election we’re ready for it,” he added.
“We have the members, the organisation and the enthusiasm. We welcome the challenge.
“It would give us the chance to put before the British people an alternative economic strategy for this country.”
Mrs May is spending three days in India laying the groundwork for an “ambitious” trade deal when Britain leaves the EU.
Speaking ahead of the visit, she said: “While others seek to tie our negotiating hands, the Government will get on with the job of delivering the decision of the British people.
“It was MPs who overwhelmingly decided to put the decision in their hands. The result was clear. It was legitimate. MPs and peers who regret the referendum result need to accept what the people decided.
“And now we need to turn our minds to how we get the best outcome for our country. That means sticking to our plan and timetable, getting on with the work of developing our negotiating strategy and not putting all our cards on the table - that is not in our national interest and it won’t help us get the best deal for Britain.”
It comes after a row over the way the backlash sparked by the controversial High Court ruling was dealt with by the Government.
Justice Secretary Liz Truss bowed to pressure from barristers to speak out in the face of intense criticism of the judges involved, but only went as far as saying the independence of the judiciary is the “foundation upon which our rule of law is built”.
The Bar Council had urged the Justice Secretary to speak out as a “matter of urgency”, saying: “A strong independent judiciary is essential to a functioning democracy and to upholding the rule of law.”
Ms Truss said: “The independence of the judiciary is the foundation upon which our rule of law is built and our judiciary is rightly respected the world over for its independence and impartiality.
“In relation to the case heard in the High Court, the Government has made it clear it will appeal to the Supreme Court. Legal process must be followed.”
But shadow justice secretary Richard Burgon said the comments were “too little much too late” and condemned Ms Truss for “failing to adequately stand up to attacks on (the) judiciary”.
“Liz Truss has still failed to condemn these attacks on the British judiciary as being ‘Enemies of the People’ and talk in the press of the sexuality of a judge,” Mr Burgon said.
“I’m afraid that it’s far too little, far too late from Liz Truss.”