The cost of living went up only 0.3 per cent last month, and the purchasing power of an average hour's work rose 0.8 per cent, the Labor Department said yesterday.

It was the fourth month in a row that inflation at the retail level has been moderate. Consumer prices have risen at an annual rate of 3.8 per cent in the last three months of the year.

But experts warned retail prices may soon start rising faster again. The problem is a recent resurgence in farm prices, which will start showing up on supermarket shelves soon.

The White House was obviously pleased by yesterday's good news. Deputy press secretary Rex Granum said the last four months of price moderation and the resulting gain in purchasing power "should help to bolster consumer spending in the months ahead."

That in turn should further stimulate economic production and help reduce the unemployment rate, which remains at 7 per cent after more than two years of recovery from the 1974-75 recession. The administration is considering a tax cut next year as an additional stimulus for the economy.

The department said supermarket prices nationally rose only 0.1 per cent in October. But farm prices went up 2.4 per cent last month after five consecutive months of decline, and some of that rebound at wholesale presumably will be passed along to the consumer.

John Layng, price analyst at the Bureau of Labor Statistics, said he was surprised there was no acceleration in consumer food prices last month, and predicted one this month.

But analysts said that does not mean a return to the double-digit inflation of the first of the year, because non-food prices ar now behaving moderately.

Prices of non-food commodities such as clothing, fuel and automobiles rose only 0.3 per cent last month. Services rose 0.4 per cent.

While the rate of inflation the last few months has been low, consumer prices were still 6.5 per cent higher last month than 12 months before, and Barry Bosworth, director of the White House Council on Wage and Price Stability, said the so-called underlying inflation rate in the economy remains between 6 and 7 per cent.

This underlying rate is essentially the difference between hourly wages and hourly output: When per-hour wages rise faster than output, businesses raise their prices to cover the increased costs.

The Labor Department's consumer price index measures the change in price of a marketbasket of goods and services thought to represent the purchases of the average urban wage, earner heading a family of four. Prices of 400 items ar collected in 51 cities across the country.

The index stood at 184.5 per cent of its 1967 average last month, which means that a selection of goods and services costing $10 in 1967 cost $18.45 last month.

Nationally, most food prices showed either small increases or small declines. Beef prices rose for the second consecutive month, while fresh vegetables fell slightly after climbing in September.

New car prices ros e0.6 per cent in October, while used car prices declined 2.1 per cent, after falling 2.5 per cent in September and 2.4 per cent in August.

Gasoline prices went up 1.4 per cent, while fuel oil and coal prices remained constant.

A big decrease in automobile insurance rates helped moderate the overall increase in services. Layng said the insurance decline in large part was due to big refunds in Massachusetts, where auto insruance rates had been boosted sharply ther earlier thi syear. The refunds represent a partial reduction.

Medical care prices rose 0.7 per cent. Electricity prices fell slightly but natural gas prices rose.

Consumers also received some mixed news from the Commerce Department. The average price of a new house declined for the first time in two years, although th 0.6 per cent dip from the first quarter to the second quarter was a small one. The average new house cost $54,000.

Property taxes, however, rose an average of 10.7 per cent in 1976, mainly because local governments. That was the largest increase since 1972.