He boasted to Conservative MPs in Tunbridge Wells that he was aware that the situation “needed to be undone” when he was in office.
And he boasted that he had instead directed money to prosperous towns like theirs.
He said he had started to change public funding formulas to ensure more places like the south-east city receive “the funding they deserve”.
The recordings, obtained by the New Statesman magazine, was from an event with grassroots Tories last week. Labor condemned as “scandalous” that Mr Sunak “openly boasted that he set the rules to transfer taxpayers’ money to rich Tory shires”.
But Mr Sunak’s campaign defended the remarks, linking it to the government’s equalization agenda. They said he had changed public spending rules to help cities and rural areas that also need investment.
In the video, Mr Sunak told Tory party members, who will choose either the former chancellor or his rival Liz Truss to be the next prime minister: “I managed to start changing the funding formulas to make sure areas like this get the funding they deserve , because we have inherited a lot of formulas from Labor that pushed all the funding into deprived urban areas, which should be undone.
“I started the job of undoing it.”
Labour’s secretary Lisa Nandy, leveling with the shadow, said: “This is scandalous. Rishi Sunak is openly boasting that he set the rules to transfer taxpayers’ money to rich Tory constituencies.
“This is our money. It must be spent fairly and where it is most needed – not used as a bribe to Tory MPs.
“Talk about showing your true colors…”
A source in Mr Sunak’s campaign said: “Level up is not just about city centres, it’s about towns and rural areas across the country that need help too. That’s what he changed in the Green Paper and he will however, follow as Prime Minister.”
“He has traveled the country and seen non-metropolitan areas that need better bus services, faster broadband or high quality schools. That is what he will deliver as Prime Minister.”
At the same event, Mr Sunak was openly challenged on his track record of pandemic support for businesses by Tory party members.
The SNP’s Alison Thewliss said: “Rishi Sunak has been honest with Tory party members about his plans for the future but not with the general public.”
In a separate video of the same event, seen by the Independent, Mr Sunak suggests people caught in the gaps in Treasury support during the Covid pandemic were not Tory voters.
He was challenged on the issue by Donna Potter, who told him, referring to the 3 million people who fell through the cracks of financial assistance from the Treasury: “If we don’t sort the gaps in support, they won’t vote Conservative at the next general election.”
Sir. Sunak replied, “As it turns out, many of them probably weren’t conservative in the first place.”
Sunak is believed to be trailing her rival Mrs Truss in the race to secure the keys to No 10.
A number of opinion polls indicate that the foreign minister has a clear margin ahead of his former cabinet colleague.
On Thursday, Mr Sunak insisted he would not drop out of the race, even though polls continue to show a huge gap between the two candidates.
Mr Sunak is running out of time to catch up. Many Tory members are expected to vote within days of receiving their ballot papers.
The next Prime Minister will be announced on September 5.