I did quite a lot of homework a few months ago. I prefer to have the phone from BT and then choose a broadband supplier, but if you prefer to have both , fine. I was with Talk Talk for years, putting up with a mediocre ADSL service .I now use Outlook.com so no need for TT e mail . I had run out of contract and was on a monthly rolling one. When FTTC came to our road , I: a) Chose Plusnet as BB super fibre unlimited. I chose the shortest contract of 12 months. They would have supplied phone as well but I kept BT for that. TT wanted £27 a month for old ADSL - Plusnet was under £25 . I am about 450 m from nearest cabinet- they guaranteed 48 mbps . Having decided, I agreed the contract with Plusnet- to start about a month later. As I was on a monthly contract they informed TT. I did formally also told TT of the decision and gave the date agreed with Plusnet. Plusnet sent router. On the day it went well . Now getting 65 mbps most of the time with a U.K. based call centre.
As long as your contract is over , there is no need for you to worry. Just check that the new supplier will keep your phone number, and you are out of contract.