Fitting an i-plate will probably not improve your BB speed in this instance but you could always try it. By the way, modern BT main sockets with the Openreach logo on them have the i-plate technology fitted in them anyway. Those older sockets with the BT logo on them do not.
If your BB speed is better when you are plugged directly into the test socket than into the front of the socket's face plate the indication is that your extension wiring is the likely cause of the problem.
Your ISP is responsible only for broadband speed up to the test socket. You would need to get an electrician to check out any extension wiring/extension sockets you might have.