The line is actually maintained by OpenReach which, although wholly owned by BT, is obliged by law to operate as a separate company. So your ISP has to get OpenReach to investigate the problem. Some ISPs seem willing to put more pressure on OpenReach than others, probably because it costs them more get their emergency repair service than their regular one. (That applies just as much to BT as to other ISPs). If you use an ISP that mainly serves business customers (such as Claranet) you'll probably get much better service than if you use one which mainly serves home users; the downside is that it will almost certainly cost you more.
You also need to consider the different 'contention ratios' used by different ISPs. You effectively share your connection to the internet with other people in your area; the more people you share with, the slower your speed. Budget ISPs generally use a contention ratio of 50:1 (meaning that 50 people share a connection at the exchange). Business ISPs are more likely to offer 12:1 or better.
The availability of 'ADSL 2+' also needs to be considered (if a fibre optic connection isn't available at your location). ADSL 2+ effectively gives you two lines connected together, thus doubling your connection speeds. As I understand it, BT home users can't get ADSL 2+ because that 'second line' capacity is taken up by 'public' signal (BT WiFi + Fon) that BT Home Hubs generate.
To complicate matters further, non-BT operator must be allowed to install their own equipment into BT telephone exchanges (using LLU = 'local loop unbundling') but physical constraints mean that only a few operators can access each exchange. So finding out which ISPs have got LLU access to your local exchange might help you find a better service.
As a guide, the more you pay, the better service you're likely to get. Most people in my street uses regular domestic ISPs, getting around 5Mbps if they're using a service with a reasonable contention ratio but with some people (using budget services with poor contention ratios) reporting speeds dropping to around 2Mbps at peak times. I use Claranet (which provides internet services to big businesses) and get ADSL 2+, giving me 10 Mbps at all times. However it costs me around £18 per month (just for internet access, with no 'add-ons' such as telephone or TV services).
You can find out what's available at your local exchange here:
https://www.samknows.com/broadband/broadband_checker