Looking through the specs for your HP laptop suggests that you were trying to plug the Ethernet cable into its HDMI port, as it seems that
it doesn't support an Ethernet connection.
http://store.hp.com/UKStore/Merch/Product.aspx?id=T1N41EA&opt=ABU&sel=NTB
So you'll need to connect via wifi, which your router supports. The documentation that Tesco provided with it should tell you the SSID and security key (= 'password') for it, although the SSID is often obvious anyway. Click the wireless network icon at the bottom right of your new laptop's screen. Look through the list of available networks and select your own. Tick 'Connect automatically' and click on 'Connect'. When you're asked for the security key, enter it and then on 'OK' (or whatever else Windows 10 calls the last bit). In future, whenever your new laptop is turned on and in range of your router, it will automatically connect you to the internet.