I know someone in Tenby about 10 doors away from me that had a BT install this week. Total cock-up from beginning. First they didn't send modem. Then the BT engineer turned up at house (which wasn't expected!), installed new Master socket, went to cab and did patching. Next he turned back up, did a test and then left. Customer went to make a phone call some time later and noticed no dial tone whatsoever!
Back on phoen to BT, luckily engineer still in area so returned. Did whatever he did and left again. Customer now has bad noise on line so in process of waiting for BT to get back to him.
His speeds fluctuating badly just as your are too!!