Might something new be stirring on the right of politics in relation to the plight of Britain's low paid? Just to pose the question is to invite ridicule from many on the left: how could the minimum-wage opposing, tax-credit cutting, VAT-hiking, benefit-squeezing Conservative party have anything to say to those at the sharp end of the jobs market?

Fair question, you might think. But take note. Parts of the right may be seeking to strike a different tone. Matthew Hancock, the high-flying skills minister – and former chief of staff to George Osborne – recently argued that Conservatives need to think afresh about low pay, and that the minimum wage should be "passionately supported" and "strengthened". He's found an echo in some unlikely places: the Telegraph published a persuasive piece in support of the living wage; then Ferdinand Mount, once Margaret Thatcher's head of policy, repeated the sentiment.

True, these are stray voices. There is little prospect of today's Conservatives rediscovering the authentic labour-friendly spirit of Harold Macmillan's middle way or Rab Butler's Workers' Charter. But there is genuine alarm among thoughtful people on the centre-right about just how out of touch the party is seen to be when it comes to the working poor.

Perhaps it won't startle many that only 9% of the public think the Conservatives best represent the interests of low-paid public sector workers; but it's telling that this only rises to 14% for those in the private sector. Given that there are 5 million workers paid less than the living wage, with millions of others earning barely more, it amounts to a towering electoral challenge.

It's hard to glean much supportive evidence on whether this nascent desire to demonstrate empathy with the low paid will find meaningful policy expression. Centre-right policy proposals for directly tackling low pay are few and far between. And while the mayor, Boris Johnson, has championed the living wage in London, Tory councils haven't followed his example (Dartford being the honourable exception).

All of which means that, as thing stand, David Cameron will be going into the next election with little new to say on this crucial issue, whereas Ed Miliband's manifesto will surely give more bite to the living (and possibly minimum) wage, as well as reducing family living costs through a major advance in affordable childcare.

The prime minister will also trail Nick Clegg: the centrepiece of the Lib Dems' election offer will be an expensive commitment to raise the personal tax allowance to £12,500 – billed as a plan to exempt those on the minimum wage from income tax. I doubt the Conservative leadership will be feeling relaxed about this. And if anyone is telling Cameron that the enormously risky universal credit – set to increase the effective tax rate for over 2 million people – can fill this political hole, then he really should be looking elsewhere for advice.

The gravitational pull of the Tory party will inevitably draw it towards a tax-cutting rather than a wage-rising response. But the options are limited. Osborne is hardly going to do a U-turn by cutting VAT; he's not much more likely to play catch-up with Clegg on the personal allowance; and the party's long awaited tax break for married couples is unlikely to stimulate the wider electorate in the way it does the Tory faithful.

Perhaps the one policy that might entice the hard-hit electorate to at least take another look at the Conservatives would be the restoration of the iconic 10p income tax band. This was the low "starter rate" on the first few thousand pounds of income that Gordon Brown introduced in 1999, then abolished in his final budget as chancellor (when the 20p rate was introduced), a decision that was to haunt his premiership.

It's hard to think of another plausible measure that could better repair the reputational disaster that was Osborne's 50p tax cut. The media would enthusiastically report it as a progressive measure (even though in reality most of the gains end up in the pockets of those on higher incomes). It would garner support beyond the Tory party as well as within it. And, fairly or otherwise, it would largely eclipse Clegg's pledge on the tax allowance (while costing far less). What's more, it has the added piquancy of righting a Labour wrong – drawing attention to the past just when Miliband will want to be focused on the future.

Which explains why the electorally attuned Conservative backbencher Robert Halfon is campaigning to get the policy adopted, and why there is speculation about Treasury interest in the idea. Halfon's argument for adopting a lower tax-rate, as opposed to a higher personal tax allowance, has impeccable Tory credentials. Nigel Lawson, Osborne's sometime mentor, started off as chancellor prioritising tax allowances. Then he changed course. "I wished to create a large constituency in favour of income-tax reductions," he later said. "The last thing I wanted to do was to reduce the size of that constituency by taking people out of tax altogether." The same thought is likely to have occurred to today's chancellor.

There are of course major – quite possibly insurmountable – obstacles. Above all, the Conservative pitch in 2015 will be "trust us to finish the job of deficit reduction", seeing through the deepest spending cuts in modern times. This hardly sits comfortably with a totemic tax giveaway, whether it's the 10p rate or another idea. Even deeper welfare cuts – resulting in more misery as well as electoral risk – would most probably be pledged to pay for it. And introducing a new tax-band would undermine Osborne's stated goal of simplifying our fiddly tax system.

And yet. Conservative leaders know 2015 will be a bitterly fought campaign with living standards at the heart of it. To have a chance of winning outright they can't just rely on fear alone, they also need to reach far beyond their comfort zone and make a big and bold gesture to those struggling to make ends meet. Labour should be warned.