Jobless John Davis, 29, took the collection boxes from shop counters on three consecutive days.
He first struck on November 9 when he was filmed on CCTV swiping a tin from a hardware store on Gloucester Road, Bristol.
The next day he grabbed a box from NatWest Bank on Bristol’s Corn Street and on November 11 he stole a tin from McColls newsagents on nearby Cheltenham Road.
At least one tin is estimated to have contained at least £100.
Yesterday at Bristol Magistrates Court David pleaded guilty to three counts of theft and one count of failing to provide a sample for a class a drug at the time of his arrest.
David Fallon, defending, confirmed he had a string of previous connections connected with his long term drug habit.
Judge Karen Shaw sentenced him to six weeks for each theft offence to run consecutively and two weeks for the refusal, to run concurrently.
She told Davis, of no fixed abode: ”There was a real and genuine loss to the Royal British Legion. It is a good cause and people work hard to raise that money.”
He was also ordered to repay the Royal British Legion £100 compensation, with the first payment on March 1.