I think 4.2km is by far and away the longest line we've got on FTTC. From the data I've got anything above about 2km is starting to get to the point of the maximum distance. Beyond that the performance is supposed to be about the same as ADSL2+. That said my line (on ADSL2+ is around 4km and syncs around 6Mbps) so in theory you should be able to get a reasonable speed.
The 40/10 service by default will sync at any speed however if it's below 15Mbps then it gets classified differently. If a 40Mbps line is unstable the line speed will be reduced through different line profiles but they have minimum speeds in some cases which could be below what the line is actually capable of (because they assume a minimum of 15Mbps). If it's below 15Mbps then the minimum speed is 5Mbps. Hopefully by trying the lower speed they will force the line to sync up but at a lower speed. If it can't achieve 5Mbps then chances are BT will want to cease if they can't fix it as 5Mbps is lowest it's supposed to be allowed to go. I've not seen any lines that low yet (low teens are the lowest I've seen but on much shorter lines). Let us know how you get on and we'll see what we can do.
Enterprise Architect - Network & OSS