The BT man came again on Wednesday, and spent about 3 hours trying to sort it out. He went to the green box a little way down the main road, and did something there, and (touch wood) it's been working fine ever since, no noise and connecting at a decent speed. He said if it happens again, to call him again and he knows of a 'broadband engineer' who could come and have a look, as it's hard for him as he doesn't have a modem with him.
Anyway, fingers crossed!
Here are a few screenies of stats etc.:
