Hi.
The Delete SMS command doesn't seem to work with my SIM800L module. If you dig into the library code, the AT command used always returns an error on this module. I've got around the issue by looking at the AT+ command standards, and discovered that the following command deletes all messages, resetting the memory index back to 1, on the SIM880L.

"AT+CMGD=1,4\r"

(The ',4' in the above command instructs the modem to ignore the index given (ie. 1) and delete ALL messages from memory.)

Hope this helps others with the same issue.