* Hammond: no-deal Brexit means no cash cushion
* Rivals Johnson and Hunt make spending pledges
* Heads down on no deal in September - Hunt
* No-deal impact would be "very, very small" - Johnson (Adds Hammond comments to BBC)
LONDON, July 1 (Reuters) - Finance minister Philip Hammond challenged the two rivals to become Britain's prime minister over their spending promises on Monday, warning that walking away from the European Union without a deal would use up the extra money in the budget.
With former London mayor Boris Johnson and foreign minister Jeremy Hunt stepping up their campaigns to replace Theresa May, both have turned their attention to how they would run a country that is deeply divided after its 2016 EU referendum.
They have promised to increase spending, particularly on public services and infrastructure, and to cut taxes, but they also say they are willing to take Britain out of the EU without a deal, an outcome that Hammond said would use up his war chest of almost 27 billion pounds ($34 billion).
"The 'fiscal firepower' we have built up in case of a no-deal Brexit will only be available for extra spending if we leave with an orderly transition," Hammond tweeted.
"If not it will all be needed to plug the hole a no-deal Brexit will make in the public finances."
Later, in an interview with the BBC, Hammond said Britain had built up a reputation for fiscal responsibility and had to live within its means.
"People have to be honest about the consequences of either spending more money or of cutting taxes," he said, warning of the "temptation to get into a bidding war".
"I think they need to be very careful about setting out these ambitions."
More than three years after voting to leave the EU, Britons still do not know whether they will leave with a deal, or without, or even leave at all.
NO-DEAL IMPACT? "VERY, VERY SMALL"
Hunt, playing catch-up with Johnson as both try to court the members of the Conservative Party who will appoint one of them, said he understood that some of the "things I passionately want to do ... will take longer" in a no-deal Brexit.
"Our immediate priority is going to be to support businesses that are directly affected by a dramatic change in our circumstances," he told a news conference in central London.
Keen to play up his "detailed" plans for both a no-deal Brexit and for leaving with an agreement, Hunt said he would try to renegotiate a deal with the EU over the summer and in earnest in September, giving himself a "hard deadline" of the end of September to decide whether he could get an agreement or not.
If not, talks would end and "we will put our heads down and focus on no-deal".
In a barely veiled reference to a rival who is often the centre of public attention, he said many Conservatives "don't want a showman, they don't want to be entertained, they want a prime minister who is going to lead us out of this crisis".
Asked how he would pay for his plans, Johnson told reporters that "the money is there ... We also think there is room to make some sensible tax cuts as well, and we will be doing that too."
Johnson, meeting voters, said his plans were carefully costed and the impact of leaving the EU without a deal would be "very, very small".
As finance minister, Hammond has helped bring down Britain's budget deficit, giving himself space to to raise the prospect of more spending and tax cuts after a decade of austerity that has helped boost the popularity of the left-wing Labour Party.
Hammond said in March that he had nearly 27 billion pounds ($34 billion) in fiscal headroom - equivalent to the difference between the target he has set himself for the budget deficit and the shortfall projected by Britain's budget forecaster.
The amount could be reduced by of a slowdown in the global economy, which is likely to weigh on Britain's output.
Britain's budget forecasters also say the headroom could be almost halved by the way that official statisticians treat student loans in the public accounts. ($1 = 0.7912 pounds) (Reporting by William Schomberg; Additional reporting by Michael Holden and Kylie MacLellan Editing by Raissa Kasolowsky)