MELBOURNE (Reuters) - Woolworths Ltd (WOW.AX: Quote, Profile, Research), Australia's largest supermarket chain, said on Friday growth in its internal rate of food inflation slowed in April, but Australia would not be immune from the rocketing cost of food globally.

Chief Executive Michael Luscombe said at a business lunch the dip in April was due to deflation in fresh fruit and vegetable prices that began in late March, while packaged grocery prices continued to rise.

"Inflation in April was back down under 4 percent," he said, compared with an annual rate above 4 percent in the retailer's internal index in the three months to March. He declined to give specific figures.

The supermarket's internal inflation figures can differ from government statistics, but provide a guide to overall inflation.

In the most recent official data, for the quarter to March, food inflation was at an annual 5.7 percent.

The rising cost of food is one of several factors pressuring Australian consumers, alongside high petrol prices and interest rates, and forcing a pullback in discretionary spending.

Luscombe said he expects that income tax cuts due in July are more likely to be saved than spent, as Australian households battle higher mortgage repayments.

"I would think that most families that enjoy those tax cuts probably have some more pressing needs at the moment," than spending on discretionary items, he said.

Luscombe said he expects further global food inflation would flow through to Australia.