Giving the British parliament a vote to "second-guess" the referendum decision to leave the European Union "is not an acceptable way forward", the prime minister's office says.
Theresa May is coming under growing pressure to allow MPs a vote on membership of the European single market, with MPs from all mainstream parties arguing that the referendum result did not amount to a vote for "hard Brexit".
Conservative MP Stephen Phillips, who backed Leave in the June 23 referendum, warned against the "tyranny" of denying MPs a vote on the Government's stance in upcoming withdrawal negotiations under Article 50 of the EU treaties.
And former attorney general Dominic Grieve cautioned that the government could be brought down if it tried to force through a new deal with the EU without MPs' approval.
The developments came as May visited Denmark and the Netherlands in the latest round of talks with counterparts from the remaining 27 EU states, designed to set out the UK's intention to maintain good relations with its former partners following Brexit.
EU leaders have so far insisted that there will be no talks on the Brexit deal before Article 50 is formally invoked - something May has promised to do by the end of March 2017.
Asked about pressure for a referendum vote, a Downing Street spokesman said: "What the Government is focused on quite clearly is making the best possible success of Brexit that we can, while acknowledging it is important that we are not blocking the will of the people so clearly expressed in the referendum in June.
"Parliament is of course going to debate and scrutinise that process as it goes on and that is absolutely necessary and the right thing to do.
"But having a second vote or a vote to second-guess the will of the British people is not an acceptable way forward."