How do I change the resolution on my LG tv to 1080p ?

Your TV is setting itself to the input signal. To display 1080P the signal must be 1080P.
"sky" souhds like your in Engalnd.
I'm in the states and have Cox cable for TV service. They only transmit HDTV @ 1080i so my TV comes up at 1080i, but if I play a blu-ray DVD in my Samsung Player the TV switchs to 1080P.

Your LG HDTV will display the full 1080p when it is available!
The resolution setting to display full HD is on always on the device that outputs.
Check the video settings on the Skybox, there should be a resolution setting there. Make sure the setting is at its highest resolution and you will be OK.

But on my old television I could change it to 1080p, and I've gone through all of the picture settings and I cannot find how to change it

Maybe on your old TV, but new TV will change it automatically by the input signal.
I remember the old TV my grandmother used to have, you have to turn a dial to change channels.

What your LG TV model?

Just because you can change it does not mean that it displayed it.
For example you can take a dvd that was recored at 760 and UPCONVERT it to 1080, But you must have the circuitry to convert it (PS it's still not true 1080, the circuit makes a "Best" quess at what the missing fram would look like.

So if a TV broadcast is sent as 1080i, you would have to have circuitry to convert 1080i to 1080P.

The guys are right and there is no way around it, the TV will display only what the output device (SKYbox) is sending it. If you have an other device like a BR or PS3 or anything else that can output full HD (1080p) just try that and then check what resolution the TV is playing at.