British businesses should increase the wages of their staff and pay the living wage for lower paid workers as they enjoy record profits in the wake of the fall in oil prices, David Cameron has said.

In a sign that the Tories appreciate they need to intensify their efforts to meet Ed Miliband’s campaign on the cost of living crisis, the prime minister said that growing profits should be “passed through” in wage rises.

The prime minister called for companies to act after official figures show that the fall in oil prices in recent months has led to a 16-year high in the profitability of companies. The figures from the Office for National Statistics showed that corporate profitability, using a measure of the return on the cost of production, was 12% in the third quarter of 2014.

Speaking in Washington, the prime minister said: “Obviously I want to see that companies’ success is passed through in terms of people seeing wage increases. It has to be done in a way that is affordable, in a way that companies can continue to grow. We need to see productivity grow. I also support, as I said in the House of Commons, the companies and organisations that can afford to pay the living wage. It is good. It also helps reduce welfare bills as well.

“The falling oil price is going to benefit a lot of businesses and a lot of countries. We want to see those benefits passed on in all the ways that they can be.”

The prime minister challenged the claim by Miliband that workers have suffered an ongoing fall in wages and living standards since the last general election. He said: “I want to see people earn money for a good standard of living. We are seeing that happening. The figures showed recently if you have been in work for a year on average people have seen a pay increase of 4%.”

The prime minister believes that the fall in the price of oil, which fell to below $45 a barrel earlier in the week before recovering to just above $50 on Thursday, will serve as a major boost for Britain and the eurozone. Officials describe the fall in price as a giant tax cut that will help stimulate the eurozone as it faces a renewed crisis amid faltering economic growth and the renewed prospect of a Greek exit from the currency the general election later this month.

Cameron’s remarks about the need for companies to pass on the benefits of falling oil prices shows that Downing Street appreciates it needs to be alert to Miliband’s lengthy focus on the cost of living crisis. But Downing Street believes that the fall in the oil price, which is creating the prospect of deflation, will eventually undermine Miliband’s campaign as even low wage increases outperform inflation.

Labour believes that the impact of years of weak economic growth, in which inflation has outstripped wage increases, has led to an ongoing cost of living crisis that will take years to rectify. Ed Balls, the shadow chancellor who was in Washington at the same time as Cameron, illustrated this point when he said on Thursday night: “You can have growth but living standards have been flat for most people, been stagnating. A short period, or even a longer period, where wages stay low but the oil price falls doesn’t get over that fundamental problem of wages not rising. The challenge is about productivity and wages. That is where the solution has got to come.”