I can't see where or how to request the transfer of an existing Giffgaff account to a new sim after the original Giffgaff sim was stolen.
Report Lost and Stolen and you will get dual/hybrid sim (micro sim pop out) with same number and credit.http://giffgaff.com/support/lost
Take a look here: http://support2.giffgaff.com/app/answers/detail/a_id/100/~/how-do-i-report-my-phone-and%2For-sim-lost-or-stolen%3F
The process is that report the SIM stolen and request a replacement - the replacement ordered through that process will automatically be linked to your number.
report sim lost for a replacement: http://giffgaff.com/support/lost
you cant port from giffgaff to giffgaff report the sim lost or stolen here to get a replacmnet sim mate http://community.giffgaff.com/t5/Help-Ask-the-community-got-stuck/How-do-I-report-my-phone-and-or-SIM-lost-or-stolen/ta-p/3487407