Solved! I have a ten year old TV with 2×hdmi sockets but no ethernet, can I use an adaptor to connect to my router?

Solution
Your TV requires a streaming stick or box such as Android TV, Apple TV, Roku, Firestick, etc to access the internet and make your old TV "smart". These will connect to one of the HDMI inputs. A computer with HDMI output will work too,
If you need additional inputs you will need to get an HDMI input selector.
Your TV requires a streaming stick or box such as Android TV, Apple TV, Roku, Firestick, etc to access the internet and make your old TV "smart". These will connect to one of the HDMI inputs. A computer with HDMI output will work too,
If you need additional inputs you will need to get an HDMI input selector.
 
Solution
It doesn't have an ethernet port because the TV doesn't have apps of its own, A.K.A. SMART. so adding a port, even if you can do it, doesn't magically wakes a dumb TV into a smart TV.

Do what americanaudiophile says.