Most sub £600 laptops have a low resolution screen, which do not match TV 1080 or 720 resolutions. The mismatch will be the cause of the blur.
Try the function button Normally (fn_+f2) or similar until only the TV screen comes on and the laptop screen turns off.
Go to display settings and change the resolution to 1080 or 720 depending on your TV
This should fix it.