British Prime Minister Theresa May has rejected the prospect of a second Brexit referendum, insisting she will not 'give in' to those calling for a 'people's vote'.

With the deadline for a final deal with the EU approaching, a number of opponents of Brexit in the UK have suggested a second 'people's vote' should be held before the UK formally leaves the bloc next March.

Several members of Mrs May's Conservative party are among those who have made the call.

However, writing in the Sunday Telegraph, Mrs May flatly dismissed such suggestions.

She argued: "In the summer of 2016, millions came out to have their say. In many cases, for the first time in decades they trusted that their vote would count; that after years of feeling ignored by politics, their voices would be heard.

"To ask the question all over again would be a gross betrayal of our democracy – and a betrayal of that trust."

In the article, Mrs May again expressed confidence that a deal would be reached - but stressed there is 'a lot more' negotiating to be done.

She observed: "It is only responsible that we have also spent time this summer preparing for a no-deal scenario, just as the EU have done too.

"For some sectors there would be real challenges for both the UK and the EU. But we would get through it and go on to thrive. So we will be ready for a no-deal if we need to be."

The British Prime Minister also said that she would not accept compromises to her government's key Chequers proposals "that are not in our national interest".

The Chequers proposals from July have been a source of tension within Mrs May's own party, and prompted several high-profile cabinet resignations - including Brexit secretary David Davis and foreign secretary Boris Johnson.

Talks are continuing between the EU and UK as negotiations enter their 'final phase'.

On Friday, the EU's chief Brexit negotiator has said that the bloc is ready to build an “unprecedented partnership” with the UK – but only if a legally operative backstop on the Irish border can be agreed.

The UK's Brexit secretary Dominic Raab said he remains "stubbornly optimistic" about reaching a deal – although he admitted the October deadline could be missed slightly.

Negotiators have been aiming to reach a deal in time for a meeting of EU leaders in October, but Mr Raab has suggested there is "a measure of leeway".