Unfortunately it's a bit more complicated - if the problem's with the copper in your street, you'll get the same no matter what internet service provider you're with, but equally some providers do have their own equipment inside the exchanges and could potentially get you a better service.
It all comes down to what the problem is exactly - there could be a range of things.
Re: your ISPs being able to activate a better speed for a while, they can change profiles, but they have risks depending on the copper you're on. For example, they might be able to switch to a higher speed profile, but it be more unreliable (drop-outs, etc) because of the state of the copper.
My suggestion is speak to your nearby neighbours and ask if you can perform a speedtest ( http://www.speedtest.net/ ) on their network to see if their ISP is any better.