You have to consider each line as seperate enitities therefore you can do whatever you like with each. There's nothing special about BT broadband, any ISP will work.
Flexible: As for not fixing things that are broken, can sympathise having gone through about 5 ISPs in 5 years.
Is Sky max is available on your exchange http://www.samknows.com/broadband/search.php
If not it's just Sky connect you can get.
Check the Ofcom Classification of your exchange on that Samknows Exchange search. If you are Market 3 there's a good chance that you can get a better deal from BT when you ask for your MAC so you can keep your existing service cheaper than you have at present.