Yes, you can do that. But before this can be done you will need to activate your gifffgaff SIM.
If you don't have the sim, you can order one from here: https://giffgaff.com/orders/mgm
To receive your sim this can take up to 2-3 working days but it shouldn't take that long.
Once received you can activate it from here: https://giffgaff.com/activate
to transfer your old number on giffgaff , you just need to click here: http://community.giffgaff.com/t5/Getting-started/How-do-I-keep-my-mobile-number/ta-p/3521127
To transfer the number you need to get the PAC code from your old services provider. PAC code is only issued by them to transfer your old number.
If you're still facing any issues while porting-in your old number on giffgaff so you need to contact giffgaff agents from here:https://giffgaff.com/support/ask/transfer
and give them the below details:
>Temporary giffgaff number:
> Keep number:
> PAC code: