LONDON, July 2 (Xinhua) -- British Prime Minister Theresa May promised Monday to roll out "detailed proposals" in a future trade deal with the European Union (EU) after Britain leaves.

"We will publish next week a White Paper with details about the proposals for our future relationship (with the EU), and that will include matters relating to customs and Northern Ireland," May said in the House of Commons when she faced a barrage of questions about Brexit.

May said her plan still involves leaving the customs union and single market, "but supports shared prosperity and security" between Britain and the EU.

"The EU and its member states will want to consider our proposals seriously. We both need to show flexibility to build the deep relationship after we have left that is in the interests of both our peoples," she added.

May insisted that Britain would leave the EU as planned on March 29 next year, despite claims that the departure date could be extended.

"There remain some real differences between us and the European Commission on Northern Ireland. So, on the protocol on Northern Ireland, I want to be very clear ... there will be no hard border between Northern Ireland and the Republic of Ireland," she said.

May's Monday statement came amid infighting among lawmakers. Responding to May's statement, Jeremy Corbyn, leader of the opposition Labour Party,told the parliament that Conservative division was having a "debilitating effect on this country and threatens jobs and communities."

Corbyn accused the government of mishandling the Brexit negotiations "every step of the way."