* Third quarter underlying sales rise 1.1 pct
* Growth was 1.8 pct in previous quarter
* New CEO to start in January
* Shares in rivals rise (Adds detail, Walmart quotes)
LONDON, Nov 16 (Reuters) - Sales growth at Asda, the British supermarket arm of Walmart, the world's largest retailer, slowed in its latest quarter, showing the tough task facing its new boss to rev-up its recovery in a cut-throat market.
Last month, Asda said Chief Executive Sean Clarke, a Walmart veteran of 21 years, would step down in January after just 18 months in the job and be replaced by head of operations Roger Burnley, a former Sainsbury's executive.
Asda and its major rivals -- market leader Tesco, Sainsbury's and Morrisons -- are all grappling with the rapid growth of German discounters Aldi and Lidl.
They are also having to cope with more expensive food imports due to a weaker pound since Britain voted to leave the European Union, while consumer spending is under pressure from rising inflation, subdued wage growth and economic uncertainty.
Of Britain's major players analysts reckon Asda was hurt the most by the rise of the discounters as its traditional price advantage was eroded.
Walmart said in February it was too slow in starting the repositioning of Asda and had not focused enough on using its leverage as a parent so that its British arm could be more aggressive on price cuts.
Asda's like-for-like sales rose 1.1 percent in the three months to Sept. 30, its fiscal third quarter -- a second straight quarter of underlying sales growth after three years of sales falls but below the previous quarter's growth of 1.8 percent, which was boosted by Easter trading.
Asda's gross profit rate declined in the quarter.
MORE WORK TO DO
"The improvements in store experience and price investments are increasing store basket sizes," said Walmart President and CEO Doug McMillon. Basket size increased 2.5 percent but customer traffic was down 1.4 percent.
Brett Biggs, Walmart's finance chief, said the parent was pleased with Asda's performance but said "we know we have more work to do."
Asda's comparative numbers were extremely weak - in the same quarter last year like-for-like sales slumped 5.8 percent. Also Asda would have benefited from food price inflation across the industry - running at 3.4 percent according to the latest industry data.
That data, published on Tuesday, also showed Asda recorded the lowest rate of sales growth of the big four in the 12 weeks to Nov.5.
Shares in Tesco, Sainsbury's and Morrisons were up 0.3, 1.1 and 1.6 percent respectively.
Last week, Marks & Spencer said its food business faced "stronger headwinds" and would slow openings of its convenience stores, while Sainsbury's said shoppers were currently "very value conscious".
On Thursday, official data showed British retail sales volumes fell 0.3 percent year-on-year in October -- the biggest decline since March 2013.
Clarke and Burnley have focused their turnaround efforts on re-establishing Asda's competitiveness by sharpening pricing in key areas such as fresh meat and vegetables, improving the quality and availability of product ranges and making its stores more attractive. Like rivals they are attacking costs. In September Asda cut 300 head office jobs.
The market environment will continue to be challenging into next year but were well placed with clear plans," Clarke said.
Separately on Thursday Walmart reported better-than-expected quarterly sales. (Editing by Kate Holton and Jane Merriman)