It is apparently possible to get some channels from other satellites using a Sky box. Click Here enter link description here. For serious viewing from other satellites a free to air box is recommended.
There will almost certainly be problems with the Sky dish. The target area for other satellites is mainland Europe so the signal level will be low in UK, usually requiring a larger dish. To continue being able to receive Astra and anoter satellite with one dish you will need offset LNBs and receiver controlled switching between them.