LONDON, Oct. 10 (Xinhua) -- MPs demanding a say in Britain's Brexit deal were told Monday that Theresa May's government will be in the driving seat.

On its first day back after a conference-season break MPs from all major parties in the House of Commons, including the ruling Conservatives, demanded they are involved in any deals with Brussels.

Leading Conservatives Labor and Liberal Democrats fired questions at David Davis, cabinet member for exiting the European Union, over the decision making processes which would see Prime Minister Theresa May and her Downing Street cabinet making the big decisions.

In a lengthy debate, Davis also warned leaders in Europe, such as France's President Hollande and Germany's Chancellor Angela Merkel, that their countries would suffer if a decision was taken to "punish Britain" for leaving the EU.

Davis made it clear the government, and not parliament, will make the decisions, using an ancient device known as the Royal Prerogative.

He told the Commons that voters gave the government a mandate that was clear, overwhelming and unarguable. Davis said the government wants the most open, barrier-free access to the European market.

He added that no one should try to thwart the will of the British people who by a 52-48 majority voted in the June 23 referendum to leave the EU.

Debates took place in both the Commons and the House of Lords during which politicians fiercely attacked the government's "go it alone" plan to invoke the exit process from Europe and reach an agreement with Brussels on future bilateral ties between the two.

Many politicians want a say on when Britain invokes Article 50, the EU rule that will trigger a two-year exit process.

The fear is that supporters of Remain could use parliamentary procedures to delay or wreck May's exit plans.

On Thursday, the High Court will hear a legal case being brought by a group of individuals who want judges to rule that parliament must be involved in the process.

Labour's Sir Keir Starmer, shadow secretary of state for exiting the EU, said in the debate that the decision taken by the government will define Britain for a generation.