Epilogue
After finally getting fed up with ntl customer support telling me how great my connection was working, I decided to switch to ADSL (nildram).
I finally got my new connection (BT line + ADSL activation, etc) just before Christmas, and from the moment I started using it, it worked fine for Skype and my VPN (just like my ntl connection used to!).
I then phoned in my disconnection request to ntl, at which point they suddenly became very interested in what my problem was (but it's a bit late then, after they forced me to go through the hassle to move to another provider
).
The upside of the whole process has been that now it looks as though I am going to cut my monthly phone+internet bills approx in half
(although there was a not insignificant cost in moving - new ADSL router required, etc) - this is partly to do with the fact that the tv part of the ntl package was worthless to me (the decoder sits idle mostly).
So I think that the only piece of wisdom that really came out of this is that if you can't get a sensible response from the normal customer services channel, they take you more seriously at disconnections!
My _guess_ is that the problem I was getting was due to a fault in the ageing terayon modem (as suggested by jonbr) that they could not detect remotely using their standard diagnostic procedures - it's a shame for ntl that they didn't send an engineer just to try a replacement.