Since you've lost your sim you can retrieve your number, as long as you have access to your account. You could perform a sim swap, this transfers all your old details (Including your number), airtime credit and remaining goodybag allowances to a new sim.
Here's more on sim swap: http://community.giffgaff.com/t5/Using-giffgaff/What-is-SIM-Swap/ta-p/7320084
report sim lost for a replacement: http://community.giffgaff.com/t5/Solve-your-questions/How-do-I-report-my-phone-and-or-SIM-lost-or-st...
or order your sim here:https://giffgaff.com/orders/mgm
sim swap, please see here:http://community.giffgaff.com/t5/Using-giffgaff/What-is-SIM-Swap/ta-p/7320084
this enables you to keep your number (and credit)
Do you mean that you don't have the IMEI number of the phone because you don't have the packaging for it anymore?
It shouldn't be a problem because if you haven't used your SIM since your phone was lost (I take it your phone was lost with the SIM in it) then the system will still have your phone logged as the last phone used (and the IMEI will still be stored).
You can select to bar your phone and SIM and a new SIM will be sent to you automatically. You can read about that here
DO NOT DO A SIM SWAP!
Report your phone and SIM lost here https://giffgaff.com/support/ask/lost_stolen_sim
This will block your phone and old SIM and start the process for giffgaff to send you a replacement SIM (with your old number and any credit etc.)
When this SIM arrives (please do not try to activate another SIM on your account in the meantime) activate it and 'away you go!'