Further to my recent questions regarding this and other related problems I can now report that despite BT's categoric assurances that "There is no fault on line", I made an engineer appointment and the guy duly came yesterday. He immediately heard that the line was noisy (which I had been saying for some time and had been denied by the BT call centre "test"), he confirmed that this noise would be enough to knock out my internet (ditto) and he therefore did some repairs at the local roadside box and fitted me a new Openreach socket. Result, problem solved, line noise gone and internet download speed up to what it should be.
He also said that the BT call centre test was a very coarse test and nowhere near as sensitive as his. His off the record comment was that the call centre make their "It'll cost you £99" threat in order to make you think and do all the recommended checks prior to committing yourself to an engineer visit.
I had a similar issue but luckily my broadband provider at the time fought my battle for me.
Mine was fine during the day but literally at 7pm every day it would drop out every 2 mins or so. Turns out my problem was to do with noise created by street lights!