You don't get to speak to the Network Services team - they are an internal team only. My understanding is that there are 3 customer facing teams: Customer Services (the people who answer the phone or webchats), Customer Relations (the people who raise complaint cases), Tech Support (the people who liase with their own internal tech & network services). The latter are the people who are supposed to manage your support case to resolution.
The best option, as they are not resolving the reported issue, is to request that you are passed to the Customer Relations team & insist that they give you a Case ID for your complaint. If they do not provide you with a resolution to your complaint (which they aren't doing), then inform them that they have not provided a satisfactory resolution and you are now at 'deadlock'. Request a 'deadlock' letter. Your letter will arrive in the post in a day or 2.
You can now refer your complaint to the Ombudsman. Go to
https://www.ombudsman-services.org/ and refer your complaint. You create a Case online and upload any evidence you have online (WebChat transcripts, images etc) and press a button to submit it to the Ombudsman for consideration.