The "big four" supermarket groups - Tesco, Sainsbury's, Asda and Morrisons - have been hit by a shift away from big weekly food shopping trips towards more frequent spending, particularly at discounters Aldi and Lidl.

The cost of fighting back against low-price rivals, coupled with a stretch of grocery price deflation, has hammered their sales and profits, while they have also had to write-down billions of pounds on the value of their out-of-town megastores.

There were signs on Tuesday, however, that the worst might be over.

Monthly data from market researcher Kantar Worldpanel showed No.2 chain Sainsbury's grew sales and market share over Christmas, the only one of the big four to do so and sending its shares as much as 4.7 percent higher.

Shares in No.4 Morrisons, meanwhile, jumped as much as 14 percent after its own Christmas trading update showed the first rise in underlying sales since 2012.

And while Kantar Worldpanel continued to show market leader Tesco losing share, there was an improvement from the previous month. That helped Tesco's shares, which hit an 18-year low in December, to bounce back as much as 7 percent. Tesco will publish its Christmas performance on Thursday.

Kantar Worldpanel showed overall industry sales fell by 0.2 percent year-on-year in the 12 weeks to Jan. 3, reflecting grocery price deflation of 1.8 percent and adding to evidence of a subdued Christmas across Britain's retail sector as unseasonably warm weather hit demand for clothing.

The British Retail Consortium said on Tuesday spending rose at its weakest quarterly rate in more than a year as stores competed to offer discounts.

But 2016 could be better for the big supermarkets.

Analysts think they are closing the price gap with discounters, improving product availability and customer service and doing better at highlighting the larger product ranges and online services they offer compared with discounters.

They also think there could be a return to food price inflation this year and that the big four should benefit from rising disposable incomes and population growth.

"All of which makes us a little bit more sanguine on the investment prospect of the UK supermarkets," said Shore Capital analyst Clive Black.

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Kantar Worldpanel said Sainsbury's total sales rose 0.8 percent year-on-year in the 12 week period and its market share edged up 0.1 percentage point. The firm attracted an additional 114,000 shoppers, with its premium "Taste the Difference" brand recording its best ever Christmas.

Sainsbury's, which revealed last week it made a bid approach for Argos owner Home Retail in November, will publish a Christmas trading update on Wednesday.

Kantar Worldpanel said Tesco, Asda and Morrisons all saw total sales fall - by 2.7 percent, 3.5 percent and 2.6 percent respectively - and all lost market share to Aldi and Lidl, which grew sales by 13.3 percent and 18.5 percent respectively.

But investors in Morrisons focussed on the firm's own sales update, also taking encouragement from reaffirmed profit guidance, a nudge-up in guidance for improved working capital and proceeds from property disposals and better year-end debt.

Former Tesco executive David Potts, who joined as chief executive in March, tasked with reviving Morrisons' fortunes, told reporters he had achieved his initial priorities of stabilising trading and running the business on lower costs. But he cautioned "we have a long journey ahead."

Also on Tuesday, sales figures from department store chain Debenhams showed it outshone rivals Marks & Spencer and Next over Christmas, sending its shares up to 18 percent higher.

Market share (percent) and sales growth (percent)

12 wks to 12 wks to pct change

Jan. 3 2016 Jan. 4 2015 in sales

Tesco 28.3 29.1 -2.7

Sainsbury 17.0 16.9 0.8

Asda 16.2 16.8 -3.5

Morrison 11.0 11.3 -2.6

Co-operative 6.0 5.9 1.4

Aldi 5.5 4.8 13.3

Waitrose 5.2 5.1 1.5

Lidl 4.2 3.5 18.5

Iceland 2.1 2.2 -4.1

Source: Kantar Worldpanel

(Editing by Kate Holton and Mark Potter)

By James Davey and Paul Sandle