Lost Phone and Lack of ID Support

Last month, my son's phone was stolen while we were on holiday. I have been trying to get the phone Blacklisted since getting back but have been unable to get through either on live chat or the phone number supplied. There is a button for blocking the SIM but we had used a local pay as you go so he still has the ID SIM and I don't therefore want to go this way. Is there any way I can get the phone blacklisted which doesn't involve ID or could I go into a Carphone Warehouse to get this done? I was going to claim on insurance but it looks like I will time out because they have quite strict timescales for the phone to have been blacklisted.