The thieves a often women of Eastern European origin working with accomplices a are believed to be particularly targeting the handbags of the elderly.
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The problem has been flagged up by police and a Yorkshire Evening Post reader.
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Acting Chief Insp Mark Bownass, of North West Leeds Division, said: "We are investigating a number of recent incidents where women thieves have distracted elderly victims to steal their handbags and purses in shops and supermarkets.
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"We urge people to be vigilant when they are out shopping and to keep hold of their handbags at all times rather than leave them in their trolley.
They should be wary if anyone approaches them and should alert shop staff immediately if they have any concerns.
"We would also ask people to keep an eye led t8 tube replacemen out for elderly shoppers and to be suspicious if someone appears to be trying to distract them."
Acting Chief Insp Bownass added: "We are working closely with shop security staff to catch and deter these criminals and in the run up to the busy Christmas period officers will be spending time in local stores to provide a reassuring presence and to offer crime prevention advice to people along with practical measures such as purse chains."
One concerned reader, Claire Radcliffe of Armley, Leeds, said: "There is a gang going round and their trick is to distract your attention and their accomplice makes off with your bags and purses."
"It happened to a good friend of ours at a supermarket at Bramley Shopping Centre on November 13 and, I understand, it was the third time that week," said Ms Radcliffe.
"She had her bag on the back of her trolley, and a Polish woman in her mid 20s asked her if the tin she was holding contained tomatoes. As she leaned over, an accomplice made off with her bag, purse containing A[pounds sterling]100, mobile phone, cards and car keys.
"It cost T10 LED Tube T10 her a further A[pounds sterling]150 and the inconvenience of having to have the car towed away and locks changed.
"They did it on an aisle that did not have CCTV so this was planned, they were not opportunists," stressed Ms Radcliffe.
"Another of my neighbours had A[pounds sterling]170 stolen out of her bag when
embroidered patches a woman pretended to feel ill in a store in Armley a my neighbour is elderly and it was the money she had saved all year for her grandchildren's presents.," she said.
"These people will stop at nothing, it is organised crime and they are trying every trick in the book to distract your attention from your
belongings.
"I urge people not let themselves become victims a educate yourself and those close to you," she said.
Ms Radcliffe said she thought the thieves were targeting stores in Kirkstall, Bramley and Pudsey but feared the thieves might move on to new targets as they become more known."
Ms Radcliffe urged shoppers to:
* Take minimal cash, cards and keys;
* Not to carry personal details including pin numbers or letters with their address;
* Use inside pockets of coats for money where possible;
* If you to take a bag a ensure it is on your person a not left in or on a trolley and ensure it is visible at all times with straps in front and fully zipped up.
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