Promises, promises. All five of the Conservative Party leadership candidates are making them, even though they know they might not be able to keep them.

Even Rory Stewart, the unexpected star of the campaign who deserves credit for highlighting the empty promises of his rivals, struggles to outline a convincing plan B on Brexit. He might be flogging a dead horse in Theresa May’s Brexit deal, and relying on dire European election results for the Tories and Labour to persuade MPs support it at the fourth attempt.

Stewart’s four opponents were also unconvincing on Brexit in general and the Irish border question in particular in last night’s long-awaited but disappointing BBC TV debate. It was clear why his media minders had wrapped Boris Johnson in cotton wool for as long as possible. He survived the hustings, but did not look comfortable under fire. He appeared to dilute his previous commitment to leave the EU on 31 October “with or without a deal”, which is now only “eminently feasible”.

Today Boris’s allies insisted his position had not changed. They would, wouldn’t they, when the eliminated Dominic Raab’s 30 votes are now up for grabs. However, these MPs might just allow Michael Gove to leapfrog Jeremy Hunt in the battle for second place. That would worry Team Boris, who do not want to face Gove in the run-off among the Tory members that will choose our next PM. Gove is already rehearsing his lines for such a contest: he pointedly told last night’s debate he was a Brexiteer before Boris.

Hardline Eurosceptics insist they have looked into Johnson’s eyes and been convinced he will take the UK out in October come what may. Friends say Boris, on the basis of his time as the EU-bashing Brussels correspondent of The Daily Telegraph in the early 1990s, has convinced himself the EU will blink under the threat of a no-deal Brexit. Put that to Brussels, and you get a different answer. Officials insist they will not suddenly show the flexibility Boris hopes for. “His timetable is unrealistic,” one told me, predicting that Johnson would be forced to seek at least a short delay beyond 31 October.

Five big moments from the BBC leadership debate Show all 5 1 /5 Five big moments from the BBC leadership debate Five big moments from the BBC leadership debate Johnson doesn't "want no deal" Responding to a question from a member of the public who fears a no-deal Brexit, Johnson repeatedly stated that "no one wants no deal" Jeff Overs/BBC via Getty Five big moments from the BBC leadership debate Candidates all agree on Tory Islamophobia inquiry After a member of the public raised the issue of Islamophobia, Sajid Javid committed to an external inquiry into Islamophobia in the Conservative Party. He then turned to his fellow candidates to see if they agreed and they all did. BBC Five big moments from the BBC leadership debate Hunt say cuts to social care "did go to care" In a surprising moment, Jeremy Hunt apologised for the extent of cuts that he oversaw in his time as health secretary. He added that local authorities need more money and that mental health care needs to improve BBC Five big moments from the BBC leadership debate Stewart alone on taxes Rory Stewart stated that he would not offer tax cuts like the other candidates as "our country is suffering huge pressure on our public services" and can not afford. He pointed out that the other candidates were offering up to £85 billion in tax cuts BBC Five big moments from the BBC leadership debate Johnson claims Zaghari-Ratcliffe comments had no consequence Following a question from a member of the public about the consequence of words, Johnson was pressed on his false claim that British-Iranian prisoner in Iran Zaghari-Ratcliffe was "teaching journalism". Johnson claimed that his words "did not make any difference" but it is widely considered that his comment led to an increased prison sentence for Zaghari-Ratcliffe. EPA

It’s not just on Brexit that the Tory candidates are overpromising. (They have forgotten Tony Blair’s mantra: it’s much better to underpromise and overdeliver than the other way round.) I have been surprised by their pledges to cut taxes, a traditional Tory tune which will appeal to the grassroots members but would leave the winner with a big headache about how to deliver them.

Stewart, again the exception, has clocked up £84bn of tax cuts offered by his rivals. Boris rowed back a little from his rash pledge to lower the taxes of those on the 40p higher rate, a rare unforced error in his safety first campaign. Now he reassures us that the lower paid would be the priority, but the total bill keeps rising.

Jeremy Hunt is promising reductions in corporation tax and employees’ national insurance payments. Yet the former health and social care secretary admitted last night that the cuts to social care budgets “went too far”. How will cutting taxes redress that? The party, and the country, deserves a more honest debate.The new PM’s in-tray will soon be bulging with bids by his cabinet for more money in an imminent government-wide review for schools, the police, defence, local government, prisons, as well as social care. That’s before living standards: a report today by the Institute for Fiscal Studies found that eight million in working households are in poverty.

No wonder Philip Hammond is kicking the treasury walls. In a letter to the leadership candidates, the chancellor warned them not to throw away the Tories’ hard-won reputation for economic competence and reducing debt. He said: “It is vital that we do not undo these achievements by making unfunded commitments that would mean debt rising again; leave the economy vulnerable to shocks; burden future generations and waste billions on additional interest payments.”

Stewart has endorsed Hammond’s fiscal rules, Gove has made sympathetic noises but the other candidates have ignored the chancellor’s missive.

The new PM would be taking a big gamble by putting tax cuts ahead of investment in public services. That would play into the hands of Jeremy Corbyn and the Liberal Democrats, a revitalised party which poses more of a threat than the Tories realise since a strong showing by them could allow Labour to win some of the Con-Lab marginals that decide general elections.