It is possible, but in order to watch different channels on the other box you would need a separate SKY viewing card.
You would also need a dual LNB for your dish in order to receive two separate signals. Look here:
http://www.tech-faq.com/dual-lnb.shtml
Its not a particularly difficult job, apart from the LNB you can get coax cable and connectors from Maplin for very little money, its just the viewing card that would be the problem because without it you will only be able to receive the free-to-air channels (BBC etc.)
Hope this helps.