53-year-old Anthony Morris from East Dulwich appeared at Croydon Magistrates' Court on Tuesday, where he pleaded guilty to theft, handling stolen goods and fraud by false representation.
He was sentenced to a total of 12 months' imprisonment for the offences.
Morris' convictions are the result of an investigation by local police officers in Lambeth and Southwark.
He first came to their attention when he stole a handbag from outside a venue along the South Bank on Thursday 16 July.
Within minutes of the theft, he was captured on CCTV at a shop on Waterloo Road using bank cards from inside the bag to fraudulently purchase mobile phone vouchers.
Morris struck again on Tuesday 11 August when he stole a handbag from a pub on Upper Ground.
On this occasion he visited two nearby shops in quick succession to make fraudulent purchases using cards obtained during the theft.
Officers were able to use CCTV from the thefts to identify Morris. He was arrested on Saturday 3 October.
While in custody, his home was searched. Property found during the search allowed officers to link him to three further bag thefts at locations across the centre of London.
Sgt Darren Watson said: "Bag theft may not seem like the most serious of offences, but it is one that causes huge upset and inconvenience for its victims and the effects go far beyond a loss of property.
"Londoners and those visiting our great city should be able to enjoy themselves without worrying that their belongings will be taken from under their nose.
"I am proud of my officers for the work that went into linking a series of offences to this one repeat offender, in particular the lead officer, PC Sarah Jackson, whose determined efforts helped to remove a prolific thief from the streets of London."