Note that channels come and go on Freesat so don't take this as 100% accurate.
One further option is Freesat from Sky which may be cheaper to install than Freesat and doesn't have a monthly subscription once you've bought the equipment. It also gives access to a few additional channels over Freesat click here
However you will have to pay a subscription to watch a subscription channel. The Freesat from Sky option allows you an upgrade path at a later stage if you wish to go that route.
Sorry I should have said your existing equipment is already a Freesat from Sky set up and you can see all the channels available there. Have you upgraded to the new white Sky Viewing Card to allow you access to FTV (Free to View Channels which require decrypting but no subscription - these are only available via Sky). If you haven't then a one off payment of £25 will allow access to these channels which ARE listed in the Freesat from Sky listing.