With Rishi Sunak behind in pre-poll surveys, one of his ministerial supporters from the UK Cabinet said on Friday that the former Chancellor could still pull off a surprise win over Foreign Secretary Liz Truss in the race to 10 Downing Street similar to the Brexit result of June 2016.

Transport Secretary Grant Shapps pointed to the outcome of the European Union (EU) referendum over six years ago, which most pollsters had predicted would end in Britain voting to remain in the economic bloc.

However, the result on June 23, 2016, confounded most analysts who had also got predictions of a Conservative Party loss or hung Parliament in general elections a year before.

We will know who the new Prime Minister is in a little over two weeks, Shapps told Sky News' when asked if it was time for Sunak to concede defeat in the Tory leadership election.

"I don't think it would be right for either side to not allow a formal vote to go ahead and if there is one thing we have learned from the last few years is, think of the 2015 election, I was party chairman at the time, everyone said we couldn't win the election," recalled the senior Conservative Party MP.

"I think the 2016 Brexit poll where everyone was pretty sure the country was about to vote for remain; I think it would be a very good idea to wait for those who are voting in this contest to complete the vote. As I said, it is only just over a fortnight's time we will know the answer to that," he said, with reference to the September 5 results day when the new Tory leader and Prime Minister will be declared.

Shapps' intervention comes a day after a YouGov poll for Sky News' suggested 66 per cent of Tory members are in favour of voting for Truss and 34 per cent back the British Indian ex-minister, once those party members who do not know or will not vote are excluded.

This gives Truss a firm 32-point lead, which most analysts have interpreted as being pretty definitive at this late stage of the contest.

Sunak, 42, himself has stressed that he is definitely in with a shot at victory as he continues to campaign to win over Conservative Party members who are voting by postal and online ballot.

However, Sir John Curtice, Professor of Politics at Strathclyde University and a leading pollster in the UK, told The Times' this week that he would be extraordinarily surprised if Truss, 47, did not go on to succeed Boris Johnson.

He did not rule out Truss' share of the vote falling below 60 per cent as Sunak gained more support among undecided members.

But below 50 it would count as a much bigger error in the polling than we've seen previously in the 2015 general election. There's a 5 per cent chance that Sunak could win it. Something would have to happen. Truss would have to foul up in some spectacular fashion. Even then it might be too late, said Curtice.

I would be extraordinarily surprised if she doesn't win. The evidence in front of one's eyes all points you in the same direction, he said.

Meanwhile, the bookie's odds also remain in favour of a Truss win, with the latest on Oddschecker aggregator putting the Foreign Secretary at 91 per cent and the former Chancellor at 9 per cent.