The tough conditions faced by families eased last month as record rainfall dampened retailers' pricing power and dragged the rate of inflation down to a 31-month low.
The wettest June since records began in 1910 saw clothing retailers bring their summer sales forward while food stores suffered from a lack of demand for barbecue meat.
The consumer price index (CPI) rate of inflation subsequently fell to 2.4% in June, from 2.8% in May, the Office for National Statistics (ONS) said.
Some economists said inflation would continue to fall - possibly below 1% - while unions said the drop in inflation was not enough as wage growth was still too weak.
Inflation has fallen from 5.2% last September to within 0.5% of the Government's 2% target, due to the waning impact of the VAT hike, falling energy, food and commodity prices, and bill cuts from utility providers.
Economic Secretary to the Treasury Chloe Smith said: "Inflation has more than halved since September, meaning a little less pressure on family budgets. This lower inflation should support high street spending and growth in the economy in the months to come."
The fall in CPI was driven by a record May-to-June decline in clothing and footwear prices, which the ONS said was more typical of the June-to-July period, reflecting earlier than average seasonal discounting. The overall rate was also driven down by transport prices, which dropped 0.5% as the price of petrol at the pump fell by 4.3p to 132.8p in June and diesel dipped by 0.7p to 135.6p.
TUC general secretary Brendan Barber said: "While the sharp fall in inflation will bring welcome relief for many workers, millions are still facing real wage cuts as the longest squeeze in living standards for decades continues. Falling inflation alone won't tackle our living standards crisis. We also need to see stronger wage growth, and for the Government to reverse damaging cuts to tax credits."
Vicky Redwood, economist at Capital Economics, said inflation could fall below 1% by the end of the year: "We think that evidence is tentatively building that weak activity and large amounts of spare capacity are bearing down on underlying price pressures."
Labour Treasury spokeswoman Catherine McKinnell said: "This fall in the inflation rate is welcome as last year's VAT rise continues to drop out of the figures. But families and pensioners are still facing a real squeeze on their incomes because of this Government's policies."