I have the 3rd generation Hex and stupid me just assumed you would be able to connect to tv via a Hdmi cable.

Seems you can't, you either have to buy a smart tv, or netgear tv thing currently at £145 on amazon or a amazon fire tv at £79.

Does anyone know of a cheaper way?

You can get budget Miracast dongles for less than £10.

I'm not sure what limitations it will have so maybe best read reviews of them or others or of the same ilk.