Since the US-Israel war with Iran began, oil and gas prices have soared, with crude up 45% to $106 a barrel.
Around 20% of the world’s oil usually flows through the Strait of Hormuz, but Iran targeting shipping through the vital waterway has effectively brought it to a complete halt.
But O’Shea said only 3-4% of the global gas supply had been lost due to the closure of the strait.
“So, the impact on gas, and therefore on electricity bills, should be lower than the impact on oil,” he told the BBC’s Sunday with Laura Kuenssberg programme.
“So my gut feel is that you’ll see more of an impact of this in the petrol pumps than you will in bills.”
Asked about government support with energy bills, O’Shea said “targeted” would be “far better than blanket help”.
On Monday, the prime minister will hold an emergency meeting with senior ministers and the Bank of England governor to discuss measures to counter the potential impact of the war in the UK, including on the cost of living.
Housing Secretary Steve Reed told the programme that the government was already taking action on energy bills, including a £53m package for homes struggling with a sharp increase in the price of heating oil.
The discussion of ways to mitigate any energy price rises came after the government’s cost-of-living tzar, Lord Walker, who is also chief executive of supermarket chain Iceland, suggested in the Sunday Times that energy companies and petrol stations should have their profits temporarily capped as oil prices jump.
But Reed appeared to rule this out, saying a cap was not currently necessary.
“We’re monitoring this, believe me, hour-by-hour,” he said. “As intervention is required, the government in making appropriate interventions but we’re already focussing on keeping bills down.”