some of the adaptors I have seen are to connect a non wireless smart tv to connect to your wireless network, but the tv must be a smart tv in the first place, so make sure the one you get does what you want, also the nowtv box I saw requires a sky subscription, its a bit of a minefield.
I would think about a cable connection as Groom suggests.
Or treat yourself to a wireless full HD smart tele

, its only taken us three months to get the hang of ours, and the wretched thing does updates to its software every month.
you can access the internet from it directly, iplayer is one touch of a button and select what you want to watch, or you can synch it to your laptop and it will just display whatever is on your laptop screen