IIRC Sky HD is only transmitted in 720p so arguing the toss over 5HD being in 1080 or not is a bit pointless. The difference between SD and 720HD is not huge to be fair. As was said before, try a decent new Blu Ray (like District 9 for example) and compare it with a standard definition broadcast. If you still don't see the difference I would suggest giving the telly away and settling down with a good book. In large print.
I reckon the problem is entirely likely down to watching a non-HD programme, despite it being on an HD channel.
There's a setting on the Sky plus box that you can turn on that shows you whether the program was filmed in HD or is just normal being broadcast on an HD channel. Changes the colour of the programmes on the planner. Also as above, buy the best HDMI cable you can, ensure your TV settings are setup properly for HD - refresh rates etc. Mine is night and day on my Philips 40" tv, and you should also be able to notice that on the non HD channels that have HD variants, the picture is somewhat dumbed down to entice you to watch the HD channel.
The DVB-T encoding for HDTV in this country has embedded error correction as part of the MPEG stream so any lost or undifferentiated bits of data can be reconstructed. Unlike audio where poor quality cable can affect digital transmission by overworking the DAC, a video signal is far less likely to literally display any fault. Typically you might see a few sparklies in the picture for a really bad cable or one which is too long, much more than that and the transmission will simply fail completely. To spend a fortune on HDMI cable is a waste of money though in such a subjective environment, the feel good factor does actually help.
Also, it's worth taking time to set up the telly properly, taking time to know what all the options do. It takes me a good few weeks of changing settings until I'm fully happy with the picture on the tellies I've had.
This is a nice basic guide that has been around a while:
Lyris Lite :: Quick and Dirty TV Setup