Alas BT is under no obligation to provide any broadband service, as you've found.
Another ISP will not alter the phone line length, but a LLU one may avoid the issues that the IP Profile, and DLM system from BT introduce. ADSL2+ will be of no use to you.
What you needed to do was some checking while the ADSL was still active, i.e. stats from the modem after just switching it on, and then again from when plugged into the test socket. The test socket (documented in front of Telephone Book) disconnects your extension wiring, which can often be the problem on longer lines.
As for your line being longer than the neighbours, it is entirely feasible, without access to attenuation, connection speeds and noise margin figures it is hard to say more. The difference in distance does not need to be massive, as ADSL is a very weak signal and a little distance difference can mean losing a lot of speed at the edges of its reach.
Ordering a re-route, if willing to pay then BT might, and by pay it may mean £1000's.