As the price war heats up, inflation at the big four supermarkets has taken another tumble.

Average inflation, as measured by The Grocer Price Index, has hovered at about 1% since February, but is now down to a new low of -0.01%.

Falling prices of key commodities like wheat and sugar have helped bring retail price inflation down gradually from more than 2.5% last summer.

But in the past three months, the supermarket price war has accelerated the process. In April, all the big four cut prices month on month and last week, Morrisons upped the ante again when it announced a raft of cuts across 1,200 lines - taking the price war further into branded territory.

The Bradford-based supermarket chain slashed prices by 1.01% month on month. In second place was Tesco, which cut prices by 0.62% while Asda and Sainsbury’s cut prices by 0.37% and 0.34% respectively.

However, year on year, Sainsbury’s has kept the tightest lid on inflation, with prices down 0.8%. By comparison, inflation at Tesco, Asda and Morrisons remain in positive territory - at 0.3%, 0.4% and 0.1% respectively.

Although prices in the majority of categories at Sainsbury’s were up year on year, overall inflation was negative because of some big reductions in alcohol and household prices. Its household prices are down 3.98% year on year and alcohol prices are down 2.34%.

The same categories are also down year on year at the other grocers - but not by the same margin. Across the big four, alcohol prices are down 1.85% and household prices 1.23%.

High levels of investment from all the supermarkets in ‘spring clean’ promotions and holiday booze deals have depressed prices in these categories.

Inflation has also eased significantly in fruit & veg and meat, fish and poultry - which have so far made up the main battleground in the price war.

Meat, fish and poultry inflation shot up to more than 7% last year in the wake of the horsemeat crisis, but this month it retreated to an annual low of 2.2%. Month on month, prices fell 1.19% with the biggest cuts at Morrisons and Tesco.

Fruit & veg inflation has also slumped into negative territory this month at -1.86% having peaked at over 6% this time last year. Month on month, fruit & veg prices have fallen 0.61%.

Morrisons - whose first round of price cuts was focused almost entirely on fresh produce - cut fruit & veg prices by 7.54% this month. Its fruit & veg prices are now 17% cheaper than they were at the start of February.