Prime Minister Theresa May met Danish counterpart Lars-Lokke Rasmussen on Monday as she faced growing calls for British lawmakers to be given a vote on her Brexit negotiating strategy.
May said in Copenhagen that she held an "excellent discussion" with Rasmussen and promised that Britain will be "a fully engaged and active member of the EU until the point at which we leave."
May was also scheduled to meet Dutch Prime Minister Mark Rutte on Monday as she steps up diplomacy to air her views of how negotiations should proceed between Britain and the other 27 EU member states.
But a growing number of opposition lawmakers and some from May's own Conservative Party are urging her to allow a vote in parliament on the government's Brexit policy.
"The country has a right to know the government's Brexit strategy and parliament must vote on it," said lawmaker Ed Miliband, a former Labour leader.
Miliband argued that the June 23 referendum did not give May a "mandate for a 'hard' Brexit," referring to any agreement that involves Britain leaving the EU single market.
May has ruled out a vote but her office said parliament would be allowed to "debate and scrutinize" the policy.
Speaking in parliament, May's Brexit minister, David Davis, argued that the government has the power to negotiate and implement Brexit without a vote in parliament, accusing opponents of seeking "micro-management" of Brexit.
"We said very clearly we want to control our borders," Davis said when asked if his government could take Britain out of the EU single market.
"We want the most open, barrier-free access to the European market." he said, adding that talk of a "hard" Brexit was "misleading."
Fellow Conservative Stephen Phillips has requested a debate on Tuesday, saying the referendum result "gives the government no authority or mandate to adopt a negotiating position without reference to the wishes of [parliament] and those of the British people expressed through their elected representatives."
May said last week that she will trigger Article 50 of the Lisbon Treaty - which sets the rules for a two-year negotiating process for a nation leaving the EU - by the end of March.
Defence Secretary Michael Fallon told the BBC on Sunday that his government will pursue a "full Brexit," apparently implying that it will not try to remain in the EU single market.
The British pound has fallen sharply against the dollar and the euro since last week, partly because of fears that the country could negotiate a "hard" Brexit.