Stabilisation period allows the system to establish the highest initial stable connection speed which is used thereafter.
One thing you can do now is test the internal phone wiring. Connect your broadband system to the internal test socket in behind the face plate in the master BT socket in your house. This will show the true speed the line will allow, by eliminating any faults in the house wiring that is causing a slow connection. If this shows an improvement then you need to buy a new faceplate with two sockets, one for broadband and one for internal phones
If ther is no improvement then contact BT and ask them to check the line between the exchange and your master socket