Whitehall1212 – The Murder Of Charles Brooks. 520106

A security guard dressed in a dark uniform is reaching for his sidearm, which is holstered on his right hip. He stands in front of a brick wall, with his left hand resting on his belt. His facial expression suggests a state of high alertness and readiness to act in case of any threat or danger.
Security Guard Drawing his Weapon --- Image by © Royalty-Free/Corbis "Used with permission from Microsoft."

Bringing you the exclusive files of Scotland Yard. Only the names of the participants have been changed.

An army private meets a stripper in a bar. Both seem to lie about who they are as they try to impress each other. On a drunken spree they steal a lorrie and becoming enamoured with the romantic fantasy of being a gangster they rob a girl. After hitting her and leaving her for dead, the matter might have been put off on the local police jurisdiction. Soon, their crime spree grows, leaving a trail of crime that draws the attention of Scotland Yard.
Though it takes a few days to track down the would be gangsters, Scotland Yard has plenty of clues, and zeros in on them quickly. Stay tuned to learn the outcome of the trial, and the way each captive pleaded that the other was more guilty than the other, drawing them into the crime spree against their will.

PS: I think this was also protrayed in the Black Museum, but I can’t recall at the moment which episode it was.