Firstly, have you reported the SIM as stolen through Giffgaff? There are two ways that we can deal with this:
1) Go to your dashboard as per this link: https://giffgaff.com/profile/details
and click "Replace my SIM" - then follow the instructions once you have your new SIM.
In regards to a SIM swap, if you want to go this option, just send me a PM with your details and I'll get a SIM sent out in the post. It will take 1-2 days to arrive.
Just to let you know: if you go via reporting the SIM as lost through Giffgaff, the only SIM that will re-enable the services on that account is the one that Giffgaff sends out, which will take about 3-5 days to arrive.
Hopefully you'll be able to get your old phone back somehow (though we won't be able to help with that).
Hope this helps!