Well, this isn't really a Wi-fi question, it's more how you can get iPlayer on your TV. There are a number of methods, but the easiest are:
1. Easiest would be to hook your laptop to your TV. The spec of your TV shows it has a PC input, so you literally just need a VGA cable (like the kind you would use to hook your laptop up to a monitor). Once connected, you'll be able to see everything you normally watch on your laptop screen through your TV. Depending on your setup, it may be easier to get a wireless mouse / keyboard and you could then easily browse to and watch the iPlayer on your TV with your laptop hidden away somewhere to keep it tidy.
2. If you have Virgin's TV service, I believe you can directly access iPlayer via the V or V+ box.
3. If you have a PS3, you can access it via the PS3's web browser and going to
www.ps3iplayer.com.
Hope this helps.