You can get BT to install a new line free by calling 0800 800 150 and ask for the 'New line free connection offer'.
It's an 18 month contract and you must make 10 calls per month but if you just get the basic call package ie. free weekend calls then any calls you make then, free, will count.
Only thing to watch is if you are still in contract with BT for line rental/call package at the moment and if this offer doesn't cover moving home.
Moneysavingexpert.com has all the info and BT advisors pop up there regularly to assist.
Unless Sky have a similar offer then there would be line installation fee (BT Openreach charge providers including BT retail around £100 for line installations, it's up to them what they charge the customer).