Boris Johnson seems to have taken Lynton Crosby’s advice, to deny any intention of calling an autumn general election once he’s installed in Downing Street – while, in fact, keeping his options open. The Tory frontrunner might also ask his election strategist what are the chances of leading the Conservatives to victory, and securing a large enough majority to implement Brexit on his terms.

Two polls out this week tell very different stories, especially about the threat from the Brexit party.

While YouGov has the Tories and the Brexit party neck and neck, on 24% and 23% respectively, Ipsos Mori shows Tory supporters outnumbering Nigel Farage’s party by more than two to one (26% to 12%).

Which is right? There is no simple answer. The big difference between the two companies is that Ipsos-Mori conducted its survey by phone, and asked respondents how they would vote, without including the Brexit party in the initial list they gave respondents. YouGov conducted its survey online and presented respondents with a list of parties including the Brexit party. By reminding people about Nigel Farage’s party in the main voting question, YouGov seems to have doubled its support.

In a general election – even more than in the election six weeks ago for the European parliament – the media will give Farage and his candidates plenty of exposure. The gap between the figures from prompted and unprompted voting intention questions will narrow. This suggests YouGov would be the better guide.

'Not the Boris we're used to': Johnson's ruthlessly organised bid for PM Read more

However, to the extent that voters feel they are choosing a government rather than making a protest, the Brexit party’s support may well be squeezed – and end up nearer Ipsos Mori’s figure.

The fate of the Brexit party’s support matters to Johnson. It may well not win a single seat. But if it siphons off enough of his voters, it could cost him dozens of Conservative seats where Labour or the Liberal Democrats came a close second two years ago. According to Ipsos Mori, 15% of those who voted Tory in 2017 would vote for the Brexit party today. That’s 2 million lost votes.

That’s bad enough for Johnson, though a strong election campaign might reduce that figure substantially. But YouGov, with its prompted question, says that 38% of those who voted Tory two years ago would back Farage today. That, for Johnson, is a catastrophic 5 million voters. Even if that figure could be halved during the course of an election campaign, it would leave dozens of Conservative MPs in marginal seats facing defeat, and could spell an early end to his premiership.

A separate YouGov survey conducted last week suggests a way Johnson could avoid that risk. Like this week’s poll, it shows the Conservatives and the Brexit party level-pegging, this time with 22% each. But YouGov went on to ask people how they would vote: a) if Johnson was prime minister, Jeremy Corbyn was still Labour’s leader and the Brexit saga remained unresolved; and b) if Johnson had already taken Britain out of the EU.

As those figures show, fighting an election once Brexit has happened would offer a huge advantage for Johnson: Farage’s fox would have been shot. Of the 5 million Tories that YouGov reckons have defected to the Brexit party since 2010, getting on for 4 million would return home.

There is one big downside for Johnson in delaying an election. Labour might acquire a new leader. Its current support – even taking Ipsos Mori’s 24% rather than YouGov’s calamitous 18% – is simply awful for an opposition party facing a government whose record is less than glorious. Ipsos Mori finds that Corbyn’s rating has fallen to the worst of any opposition leader: worse, even, than Michael Foot at his lowest point. A new leader might restore the party’s fortunes.

Johnson’s choice, then, is whether to strike early, while Farage is a threat but Corbyn isn’t – or strike later, post-Brexit, with Farage’s balloon punctured but Labour possibly revived. If I were advising Johnson, my judgment would be that delay is the lesser risk – but it’s no guarantee of victory.

• Peter Kellner is former president of YouGov