Mr Hammond made the suggestion during a spring statement designed to build support for Government efforts to break the Brexit deadlock.
He said that a no-deal departure could have wiped out the expected windfall and risked a return to austerity.
The statement was given amid parliamentary chaos following the rejection of Theresa May’s EU Withdrawal Agreement by MPs on Tuesday.
Mr Hammond said: “A brighter future is within our grasp. Let’s take a decisive step towards seizing it and building a Britain fit for the future, a Britain the next generation will be proud to call their home.
“It is an economy that has defied expectations and will provide the solid foundation that Britain needs to seize the opportunities that the future offers. If we leave the EU with a deal and an orderly transition to a future economic partnership, we will see a deal dividend.”
The Chancellor revealed that rapid wage growth above the rate of inflation had led to unexpectedly high Treasury income from tax receipts.
The extra cash meant the Treasury could look forward to extra “headroom” above his commitments for cutting Government borrowing worth about £26billion by 2020/21.
The figure was £11billion higher than forecast at his last Budget in October.
He earmarked the windfall for “keeping taxes low” and finding extra funds for the NHS, the social care system, schools and the police.
Warning of the dangers of a no-deal Brexit, the Chancellor added: “Leaving with no deal would mean significant disruption in the short and medium-term and a smaller, less prosperous economy in the long-term, than if we leave with a deal.”
Voters had not backed “higher unemployment, lower wages, higher prices in the shops” when they opted for leaving the EU in the 2016 referendum, he said.
Far bigger sums for public services could be released by a Treasury Spending Review for the next three years to be published at the Autumn Budget as long as the country left the EU with a deal, he said.
Mr Hammond warned that further Treasury spending would have been put at risk by a no-deal Brexit.
The Chancellor also used his statement to unveil an extra £100million for overtime payments for police forces in England to help tackle the “epidemic” of knife crime.
He also announced a £3billion scheme to help build 30,000 affordable homes and declared a new green target of banning fossil fuel heating systems in all new houses constructed after 2025.
Tuesday’s Commons vote rejecting Mrs May’s revamped Brexit deal meant “we are not where I hoped we would be today”, the Chancellor said.
He added: “Our economy is fundamentally robust but the uncertainty that I hoped we would lift last night still hangs over us.
“We cannot allow that to continue.”