This number is attached to a postal scam in which cards are posted suggesting the receiver has to call a number to arrange the re-delivery of a parcel.
However this is not from the Royal Mail it is from Parcel Delivery Service (PDS). Charges for calling this number are astronomical. Do not phone the number 0906 6611911.
This scam has even been picked up on and shared by the US embassy in London:
Postal scam notice: A card from “Parcel Delivery Service” with a phone number of “0906 6611911” is a premium-rate postal scam!
— U.S. Embassy London (@USAinUK) October 17, 2008
A card thru the door from PDS saying they could not deliver a parcel – ring 0906 6611911 premium rate SCAM SCAM SCAM SCAM if you ring it just cost you £315 SCAM SCAM SCAM SCAM
— michael john holt (@Holt10John) October 5, 2020