Hi,
i am a ex BT engineer, and work for myself. Firstly, when the line is tested, 99% of the time it tests o.k. even though there is no dial tone at the customers premises.
the one and only way is:
Go to the master socket. if it is a modern one, it will have a "split face" .
undo the two small screws and pull out the lower part of the faceplate. do this carefully, as all extension wires SHOULD be connected to that. you will then see another phone socket inlet on the right hand side of the remaining part of the socket. you need to plug a wired phone ( not walkabout wireless phone) into that socket and dial "1". it should be silent for several seconds, no crackling or humms. if it is noisy in any way, then the fault is with BT, BUT, check the wiring to that socket, it may come in from an overhead connection, or from underground, or go into your loft. you need to make sure the wiring is in good condition, and not damaged by you or a previous teneant/owner.
If you are sure the wire is the way BT left it, then phone them( or whoever you pay your line rental to) tell them you are testing from the master socket and you still have a problem
if all is well, then you need to plug your router/hub/modem into the test socket on the nte5 ( thats the BT name for the master socket) and monitor the ADSL light. it must stay constant and not flash, change colour or go out and come back on at intervals. If it stays constant, and all the problems have gone, then get in touch with me and I will direct you on how to test and rectify your internal wiring. I have a help page on my web site, but I think it would be seen as advertising if i listed it here. Filters are sometimes a problem, so change the one you use for your modem. Also, do the normal test practise, unplug everything from every socket in the house, especially if you have a sky box plugged onto the phone line, (if you have an alarm connected to the phone line, is it filtered?) and see if that cures the problem. there are a shed load of things that interfere with broadband, cables run beside micro wave ovens, cables run alongside fluoro lights, cable being too close to aerial cables. these problems are worse if you are on the outer brink of the signal, say about 2 to 3 miles from your telephone exchange and your normal signal strength is only around 1 to 1.5 Mbs. If you had signal of 6Mbs, then you could probably use wet string instead of wires.
i must just add, that the main reason for doing all these checks, is that if your service provider has to call BT out, and the fault is in your property, because you are using cheap extension DIY cables, or the dog has chewed something, then the cost will be around £ 130 call out and £90 hour to put it right. Advice is FREE.
Percy.