the constant drops in connection are the reason for your slow speed.
are you able to use the test socket
Ok so only wires connected are on terminals 2&5? Any chance you can borrow another filter to try especially if you have no other phone sockets in your home
try quiet line test. Dial 17070 option 2. Should be quiet and best done with corded phone
ive looked into the socket there are 6 terminals
terminal 2 has two wires connected
terminal 3 has one
terminal 4 has one
terminal 5 has two
Is that the master socket? You only need terminals 2&5 connected in both sockets. However I would have expected 2 wires on terminals 2&5 so your extension socket works so does extension socket actually work?
the bell wire on terminal 3 can cause problems.
If the problem is being caused by your internal wiring then unfortunately you may be charged the callout fee for engineer visit of £129.99.