Food price rises pared back last month as retailers tried to protect shoppers from inflationary pressures.
Overall shop price inflation was 0.4 per cent in July, according to figures from the British Retail Consortium (BRC), and food price inflation fell to 1.2 per cent from a rate of 1.4 per cent the month before.
Non-food retailers haven't started increasing prices yet. Prices fell by 1.5 per cent, which the BRC said was due to businesses trying to keep prices low where possible.
However, retailers would not be able to absorb the increased cost of importing indefinitely, the industry body said.
Sterling-related price rises have impacted food retailers faster than non-food retailers because food stock cycles are shorter.
It is thought that prices on clothing, furniture and other items will start to feed through soon, but competition in the non-food sector is helping to keep price rises in check.
In the coming months, consumer spending may be restrained by price pressures on other essential items.
"The government should be doing all it can to avoid further, potentially significant, increases in the cost of living from a failure to reach a deal with the EU that ensures no new tariffs and secures a fair Brexit for UK consumers," said Helen Dickinson, BRC chief executive.
Tariffs on key EU imports such as cheese and beef could shoot up if Britain leaves the EU without securing a trade agreement. The BRC has warned that effective tariff could jump by as much as 80 per cent on some items.