The letters threaten to spread false rumours about the recipients being paedophiles unless they deposit Bitcoins, a form of online currency, into a specific account.
Eleven people in Maidenhead, Bourne End, Hedgerley and High Wycombe, have reported receiving the letters, which police think may be connected.
Extracts from the letters read: "If you do not follow these instructions to the letter you and your family will be subjected to a campaign which will include writing to your neighbours informing them of your love for young boys.
"You know what will people will think once we put the idea in their heads? No smoke without fire is what they will think."
Detective sergeant Peter Wall from Force CID Maidenhead, said: "Some people may simply discard letters like this when they receive them but for others it can be very distressing.
"This is a clear attempt at blackmail and we need to gather all the information we can to aid our investigation and trace the offenders behind these nasty letters."
Contact the police on 101 or Crimestoppers anonymously on 0800 555111 if you have information.
Top Ten Articles
The Met Office has issued a yellow alert for Windsor and Maidenhead, Slough and Wokingham, warning that rain moving eastwards across the south of the country may turn to snow in some places.