I recently left Talk Talk after it would drop out countless times a day, i always find there is two ways to deal with broadband providers.
Either try to boost your package and get fibre optic or something for a discount price for being a long term sky customer. (I imagine you wont want to pay more than you already are so mention that).
Also, They would charge you a leaving cost depending on how long is left on your contract, You can either choose to buy them out and change providers or just complain and complain and put loads of issues on you record to show that you are clearly having problems. With my Talk Talk, our leaving costs were £200+ since we still had a good year or so left with them, but we just phoned up over and over again, supervisor to supervisor until they let us go for free.
Moral of the story, If you want them to do something for you, keep talking to supervisors (they seem to do, and care more than regular staff) and just make sure they record that you are deeply unhappy with the service, if they try to blame things on you don't take it since they should be providing an adequate service. If they want to keep you then they should either fully fix it, or boost your package.