The version that works is sending an 11 digit phone number. The version that
doesn't is sending a 16 digit number that may or may not be in ASCII format.

Does this work?
Code:
   TelephoneNo1 var byte[16]
   X VAR BYTE
   Y VAR BYTE

    FOR X = 0 TO 10    ' 11 digit phone #
      LOOKUP X,["07771716175"],Y
      TelephoneNo1[X] = Y
    NEXT X

   hserOUT [65,84,13] 'Sending "AT" and Carraige return to GSM module
   hserin 5000, SMS,[WAIT("OK")] ' wait for response ok for 5 seconds 
   hserOUT ["AT+CMGS=",34,str TelephoneNo1\11,34,13] 'Here the GSMmodule is told the desitnation phone number
   hserin 15000,SMS,[WAIT(62)]
   hserOUT ["WJ Groundwater Limited One Pump Failed",26]
   hserin 15000,SMS,[WAIT(43,67,77,71)]