Griffith – who was appointed as shadow chancellor last month – told the BBC, Labour had raised taxes at its last two Budgets and that the “pips are well and truly squeaking”.
In addition to ruling out tax rises, he said the government should “pause job-destroying red tape” adding: “Whatever its intentions it is causing a real chill in the vacancy market.”
The Conservatives pointed to figures from the Federation of Small Businesses estimating that tax compliance costs small businesses £25bn a year and the average small business spends 44 hours a year on tax admin.
The party has appointed Lord Mackinlay of Richborough and Robert Colvile, the outgoing director of the Centre for Policy Studies think tank, to produce a report on reducing regulations for small businesses.
Griffith said governments have to “balance the books” and that the Conservatives would change the welfare system, “prune” back the amount spent on foreign aid and cut “some of the central cost of Whitehall” in order to save money.
Over the weekend, the Mail on Sunday reported, external that the Conservatives could promise to abolish inheritance tax if they win the next election, with the policy potentially being announced at the party’s annual conference in October.
Asked if he would be taking such a move, Griffith said there was “work to be done” adding: “We’ve got to fully find the money.”
“I’m going to be responsible and only want to make promises I can keep,” he said.
He added that he had recently been on a fact-finding trip to Sweden, which scrapped inheritance taxes in 2005.
Reform UK has previously said it wanted to cut inheritance tax, but speaking at the party’s conference, Treasury spokesman Robert Jenrick said it would not be a priority.
“It’s a bold chancellor that would say I’d rather privilege 36,000 families than 40 million [income] taxpayers,” he told a Reform conference fringe event.
Asked if getting rid of inheritance tax would amount to a tax cut for the wealthy, Griffith argued that it would boost growth and that the wealthiest people were often able to “arrange their affairs” to avoid the tax.
