Tesco.net being slow isn't a big shock in itself, I get several times faster speed tests than a tesco user up the road (who is closer to the exchange and has a similar sync speed).
Taking the phone off the hook can improve some types of line fault, as it draws extra current through the line and joints. If this is going to have an effect it should show up in the sync speed increasing on the modem/router, hence allowing a faster throughput (if everything else keeps pace).
So to go further we need to know if the modem speed changes when the phone is off the hook, or some further clarification of what exactly happens when the phone is off.
MaxDSL - goes as fast as it can and doesn't read the line checker first.