Prices are continuing to rise at their fastest rate for 40 years with food costs, particularly for bread, cereal and meat, climbing.
The Office for National Statistics (ONS) said inflation edged up to 9.1% in the 12 months to May, from 9% in April,
Fuel and energy prices are the biggest drivers of inflation, but the ONS said food costs had pushed it up further.
Workers and unions are pushing for pay rises to cope with higher prices.
But the government has warned against employers handing out big increases in salaries over fears of a 1970s style inflationary spiral where firms hike wages and then passed the cost onto customers through higher prices.