A 75-year-old woman was shopping in Waitrose, in Rectory Road, Wokingham, at about 1pm on Friday, March 15, when she was approached by a man and woman who said she had dropped £10 - engaging her in conversation.
A few days later she realised that her card was missing and £2,400 had been taken from her account.
The offender is Asian, possibly of Pakistani origin, between 20-25 years-old, 5ft 8ins, and of slight build.
He was wearing black trousers, a black coat with a mandarin collar, and the victim described him as very smartly dressed.
The woman with him appeared eastern European, aged about 25, with shoulder length curly hair.
She was wearing a short leather jacket and trousers.
A similar incident took place at about 10.50am this Monday, March 25, when a 77-year-old woman was shopping in Superdrug in Crockhamwell Road, Woodley, at about 10.50am.
She was approached by two people of the same description.
After interacting with the couple - who again suggested she had dropped £10 - the victim realised a short time later that her card was missing.
She reported it stolen to her bank and found £460 was gone from the account.
PC Jonathan Turner-Evans, investigating the incident, said: "These were despicable crimes, targeting elderly people and stealing large amounts of money from their accounts, after making it seem like they were carrying out a good deed.
"We believe the same people are responsible for both thefts and are keen to trace them. I would urge anyone who saw either incident, or recognises the descriptions of them to contact me.
"I would also like to make members of the public aware that these people are operating in the area and ask them to be specially vigilant with their purses and bank cards."
Anyone with information should contact PC Turner-Evans on 101 or, to remain anonymous, call Crimestoppers on 0800 555 111.