The Labour leader revealed his position during a visit to Shipley in West Yorkshire, just days after Theresa May said she could not answer the question because she would have to weigh up the evidence again.
In contrast, two senior Conservative ministers, Liz Truss and Jeremy Hunt, have said they have changed their minds since the Brexit vote and would now opt to leave instead of remain.
Asked if he would vote remain if a new referendum were held tomorrow, Corbyn replied: “There isn’t going to be another referendum, so it’s a hypothetical question but yes, I voted remain because I thought the best option was to remain. I haven’t changed my mind on that.
“But we accept the result of the referendum therefore we want to make sure we obtain tariff-free access to the European markets and protection of all the rights and membership of agencies we have achieved through the European Union membership.”
He also said Labour was extremely concerned about the lack of progress made in the Brexit talks and the possibility that the UK could crash out of the EU with no deal.
“The danger is we will get to March 2019 with no deal, we fall out of the EU, we go on to World Trade Organisation rules and there will be threats to a lot of jobs all across Britain,” he said. “I think it is quite shocking. We are now 15 months on since the referendum and the government seems to have reached deadlock at every stage,.”
Commenting on the end of the fifth round of talks in Brussels between the Brexit secretary and the EU’s chief negotiator, Corbyn said: “Every time there’s talks between David Davis and Michel Barnier, both come out making opposite statements. David Davis says it’s gone well and Michel Barnier says it isn’t. They can’t both be right.”
Keir Starmer, the shadow Brexit secretary, has written to Davis urging him to make progress before the European council of ministers meet next week.
This article was written by Rowena Mason Deputy political editor, for theguardian.com on Thursday 12th October 2017 15.39 Europe/Londonguardian.co.uk © Guardian News and Media Limited 2010