To watch HD, you need 2 things - first, a HD TV (which you've got). Second, a HD source to feed into the TV. A Sky+ Box is not a HD source (but you can still watch TV from it in normal definition). A Sky HD box is a HD source, though only certain channels are broadcast as HD (although you can still watch the others in normal definition). Several other things are HD sources - for example, a BluRay player, some games machines (PS3, Xbox, etc) , some computers, and a few other devices.
If you don't want to fork out more cash for Sky HD, HD Freeview is coming to certain parts of the country by March 2010. Your new TV should get this if you're in the right area. If not you may have to wait until 2012.