Generally all providers of phone services (except cable providers) use BT's line equipment .... however .... the ringing and caller ID signal is part of TT's setup .... so if there equipment isn't putting out the correct signal or voltage .....
the biggest difference is BT has engineers everywhere whereas the small operators may not have a guy within 50 miles of you ....
I'm not implying that talk talk do this .... but some operators will ignore the first 2 or 3 reports (if the fault requires an engineer to visit) as most "missed calls" or intermittent facility faults clear themselves - or are due to the far end.
(how else can they keep costs down?)
I personally have stuck with BT and .... while it hasn't been trouble free .... Friends have had far far worse experiences elsewhere.
You should start by getting your line checked (again??)
and then it's tough love .... low bills ....or .... better service??