LONDON, April 3 (Xinhua) -- Talks between British Prime Minister Theresa May and main opposition leader, Labour's Jeremy Corbyn, to break the Brexit logjam were described Wednesday as constructive.

The two big political rivals plan more talks Thursday aimed at finding a deal that can be put to the House of Commons to pave the way for Britain's departure from the European Union (EU).

The two were said to have agreed a program of work, with a spokesperson at 10 Downing Street saying Wednesday night that both sides had shown flexibility.

The spokesperson added both sides also gave a commitment to bring the current Brexit uncertainty to a close.

In a statement after the meeting with May concluded, Corbyn said, "There hasn't been as much change as I expected, but we will have further discussions tomorrow (Thursday) to explore technical issues."

"I put forward the view from the Labour Party that we want to achieve a customs union with the EU, access to the Single Market and dynamic regulatory alignment, that is a guarantee of European regulations as a minimum on the environment, consumer and workers' rights," Corbyn said.

"I also raised the option of a public vote to prevent crashing out or leaving (the EU) on a bad deal," he said.

May announced Tuesday night that she wanted to hold talks with Corbyn after a seven-hour cabinet meeting of her senior ministers. She also said she would ask the EU for a short extension to the current April 12 departure date.

Two of May's ministers resigned Wednesday over the way Brexit was being handled by the prime minister. She also came under attack from a number of her own Conservative MPs for agreeing talks with the Labour leader.

Media reports in London claimed that at Tuesday's marathon meeting a majority of May's ministers favored Britain leaving the EU with no deal.

On Wednesday, MPs started a debate on a backbench move to introduce legislation that, if backed by a majority of MPs would rule out Britain leaving with no deal.

The debate went ahead after a majority of just one when MPs voted to decide if they wanted it to go-ahead.

The vote of 312 to 311 means a draft Bill brought forward by backbench MPs which would force May to seek a Brexit delay beyond April 12 to avert a no-deal outcome.

Britain has until April 12 to propose a withdrawal plan to Brussels which must be accepted by 27 member states of the EU. If it fails Britain faces leaving on that date without a deal.

In an interview with Sky News, Mark Carney, the governor of the Bank of England, said the risk of a no deal Brexit was now alarmingly high.

"We're in a situation where the expressed will of parliament is for some form of deal, so to put it in the double negative: parliament is against no deal," he said. "The government, as expressed by the prime minister, is against no deal, the European Union is against no deal, and yet it is a possibility -- it is the default option."