Connections to FurtherLink are made via a DNS record pointing to the pi-top local IP. Some ISP DNS resolvers don’t accept this, so we recommend Cloudflare DNS and configure it by default on pi-topOS currently.
As this configuration is not causing issues on your pi-top it seems that your network can allow it, so possibly you have not configured Cloudflare DNS correctly on your PC. If it is configured correctly and not blocked you should be able to confirm this at https://1.1.1.1/help.
Other alternative DNS providers such as those listed here should also work.
If the DNS connection to the pi-top can be made, you should be able to confirm it by opening these links in your browser (with the dash (-) delimited local IP of your pi-top in them):
http://192-168-1-137.further-link.pi-top.com/ (opens the web ui tour)
https://192-168-1-137.further-link.pi-top.com:8028/status (further-link status, should respond ‘OK’)