Several members of the public have told police they were visited by a woman claiming to be seeking sponsorship for a charity walk in aid of Help for Heroes.
The woman is described as white, around 5ft 10ins tall, of slim build, with shoulder-length mousey brown hair and bad teeth.
Officers believe the fraud has been committed over a long period of time in various other areas and there are potentially many more victims who are unaware they have been scammed.
Police believe both commercial and private addresses have been targeted many areas including Clowne, Whitwell and Worksop.
A woman in her 30s has been arrested on suspicion of fraud and is currently on police bail.
Officers are reminding residents not to hand over cash on the doorstep unless they know the person and if they want to donate to the charity do so directly by other methods.
Anyone who thinks they may have been a victim of this type of fraud is asked to contact PC Emily Sunderland on the non-emergency number 101 or Crimestoppers anonymously on 0800 555 111.