Chief Executive Dave Lewis has cut prices on fresh produce and branded goods, as well as improving customer service and product availability, in an attempt to win back the customers that have deserted it in droves for cheaper rivals Aldi [ALDIEI.UL] and Lidl [LIDUK.UL].

Shares in Tesco rose 2.7 percent on Tuesday after data from Kantar Worldpanel, an industry market researcher, said its sales nudged up 0.3 percent over the 12 weeks to Feb. 1 when compared against the year-ago period.

That small rise nonetheless considerably outperformed Asda, Sainsbury's and Morrisons, where sales fell 1.7 percent, 1.0 percent and 0.4 percent respectively.

"Tesco is bouncing back from a tough year, with Dave Lewis’s efforts to overhaul the supermarket attracting an additional 236,000 shoppers into its stores in the last 12 weeks," said Fraser McKevitt, Kantar's head of retail and consumer insight.

In addition to changes on the shop floor, Lewis also announced last month that he would slash internal costs and sell assets to mend the company's finances and fight back from years of market share losses and debt-ratings downgrades.

He still has a way to go regarding Tesco's market share, which Kantar said fell 0.2 percentage points to 29.0 percent as discounters Aldi and Lidl continued to gain ground, with sales growth of 21.2 percent and 14.2 percent respectively.

However, the positive sales news follows a better-than-expected Christmas for Tesco, which said in January it had seen volume growth over that period for the first time in five years.

Analysts at Barclays concluded the back-to-back figures suggested "The longer-term trends (for Tesco) are clearly more encouraging than they have been for some time."

Overall spending in Britain grocery market grew at its fastest rate since June 2014, up 1.1 percent over the 12 weeks, while like-for-like prices fell by 1.2 percent.

“Shoppers are taking advantage of both lower fuel prices and the continuing price war among the supermarkets to slightly increase their grocery spending," said McKevitt.

Elsewhere in the sector, shares in Morrison jumped 6.2 percent after its sales performance, though down, hit its best level since December 2013.

Alongside Tesco, Sainsbury's and Morrisons also published Christmas trading updates last month. Both came in ahead of analysts' forecasts. Asda will update on its fourth quarter on Feb. 19.

(Additional reporting by Neil Maidment; Editing by Sophie Walker)

By James Davey