The UK's biggest supermarkets have launched a range of price cuts.
On Monday, Morrisons said it would cut prices by an average of 20% on 935 products, including tinned tomatoes, cereals and multivitamins.
Also on Monday, Tesco, which is celebrating its centenary, said it was cutting the price of hundreds of products this month in some cases by more than 50%.
Sainsbury started its New Year price promotion last Wednesday.
John Lewis-owned Waitrose also has some deep discounts on offer, some with prices down by more than 30% on a range of goods, from tea to toothbrushes.
But it said this is simply one of its regular promotions, which are planned in advance and are not part of any concerted price competition.
Tesco said in a statement: "Today, to celebrate our centenary and to mark 100 years of great value, we're reducing the price of hundreds of products across the month."
Morrison's Andy Atkinson, said: "We're listening to customers who are telling us that their budgets will be stretched in January, so we are cutting every penny we can on the essentials."
Duncan Brewer, retail partner at consultants Oliver Wyman, told the BBC that retailers did not have much room to cut prices further: "The grocers' margins are low by historical levels, so they have limited room for manoeuvre, given the impact of the discounters over the last decade.
"While they will continue to fight for every customer, without a major step-change in their cost-base, they will find it hard to keep investing in ever-lower prices."
This week, many of the biggest names in UK retailing will reveal their Christmas trading figures, with Morrisons' own update due on Tuesday.
Sainsbury's will reveal its Christmas performance on Wednesday and Tesco on Thursday.
One of the threats to the established UK supermarkets remains the German discounters.
The scale of this was underlined by figures out on Monday from Aldi, which said its sales rose by 10% in the run up to Christmas and reached a record of almost £1bn in December.
It currently has 827 stores and plans to continue growing. It expects to have 1,200 stores by the end of 2025.
Meanwhile, Selfridges reported a good Christmas, sales were up 8% in December compared with those of 2017.
It said its range of in-store entertainment, which included pop-up choirs, helped pull shoppers into its physical stores.
Homeware chain Dunelm also released a statement on Monday. It said it expected first half profits to be higher this year than last, as long as sales continued to rise at their current rate.