Problems with broadband line speed on a BT line.

I live in a new house only a matter of a few hundred yards from the telephone exchange and BT have assessed my line speed as the likely maximum speed is 500KBS. All my neighbours line speed assessments with BT are up to 8MB/s.
My computer is modern and fast and I am hard wired to a Netgear modem which is capable of working at 108MB/s. I have changed all my modem filters in my house and tried a new modem router and this has made no difference to the speed I receive of broadband in my house. I have even tested the line via the BT test socket where it comes into the house and this has made no difference to the speed. Some days I can only get speeds of 400 to 500 KB/s and on others it goes up to over 6MB/s. Because I work shifts I have done speed checks on my line at all times of day and night and this seems to make no difference at all. For example I still get the slow speeds in the middle of the night. My fast download speed does not stay very long (a day or so) before it drops back to less than 500KB/s. Can any one please help me and tell me why my line speed is going up and down so dramatically and what the problem is. I know BT have assessed my line as only able to achieve a maximum likely speed of 500 KB/s but surely that cannot be right if speedchecks have shown that at times I get over 6MB/s.
I have checked with BT and I have no DACS on my line and as my modem router is secure I know for certain that none of my neighbours are tapping into my broadband through my modem router.
My ISP until very recently was Virgin but they were not much help in getting this resolved and I ended up spending

When BT say there is no fault on the line, they are talking about the line's suitability for voice, not broadband. Because you buy your broadband from Sky, they are the ones who you must contact to get the line checked. BT will not talk to you directly, because Sky are their customer, not you.