Hi,
i am a self employed telephone engineer, and deal with broadband problems all the time.
first question: what time of day does this happen, or is it anytime? if it's evenings, then it may be too many people on line at the same time, or that your ISP has throttled you back because you were using too much bandwith, by watching you tube, I player etc.
next question: if you have used the test jack in the master socket, are you sure that the cable feeding the master socket does come straight to the socket, and has not been interferred with somewhere? ( if its overhead feed, look at the cable from the pole to the house, if it goes into the loft, then it needs investigating to make sure it goes straight to the master socket, and that there are no cut ins on the cable, or junction boxes etc. with other cables going to extension sockets)
Next: where the BT cable comes through the wall, is it only the BT cable, or are there other cables in the same hole? such as aerial cables etc.
Next obvious question: have you " unplugged the new phone and tried the speed from the test jack then plugged it back in again? ( to the filter) and tested again.?
Do you have a sky box plugged into the phone circuit?
I must just add that all sorts of things can cause problems, such as wires run next to fluoresecent fittings. microwave ovens, and sky boxes are a real bummer, a great big metal box picking up all sorts of interference, but not normally when the signal strength is good, and 4Mbs is quite reasonabale.
Percy.