Router constantly reconnects resulting in slow spe...

Question

My router (I think it's a home hub 3) disconnects and reconnects frequently. After a reconnection my measured download speed drops from 4.5 mbs to 0.45 mbs. After some while it returns to the normal 4.5. This used to happen only rarely, but now it is happening several times a day so that I almost always am faced with the 0.45 download speed. I have no exptension lines in the house - only the master socket. I have opened this up and connected directly to the test socket with no improvement - still reconnects every few hours. It may be that this happens more frequently during windy/rainy weather, but I can't say for sure.
From the event log at most recent reconnect:
 07:29:05,12 Dec.
QoS Rate cap set to 0.4Mbs
  07:29:05,12 Dec.
WAN connection WAN1_INTERNET_B_ATM2_0_35 connected.
  07:29:04,12 Dec.
DSL Link Up: Down Rate=6016Kbps, Up Rate=448Kbps; SNR Margin Down=15.1dB, Up=23.0dB;
  07:28:55,12 Dec.
WAN connection WAN1_INTERNET_B_ATM2_0_35 disconnected.[ERROR_NO_CARRIER]
And now (4 hours later):
ADSL Line Status
Connection information
Line state:
Connected
Connection time:
0 day, 04:20:53
Downstream:
6,016 Kbps
Upstream:
448 Kbps
  ADSL settings
VPI/VCI:
0/38
Type:
PPPoA
Modulation:
G.992.1 Annex A
Latency type:
Interleaved
Noise margin (Down/Up):
15.3 dB / 23.0 dB
Line attenuation (Down/Up):
29.0 dB / 17.0 dB
Output power (Down/Up):
20.1 dBm / 12.4 dBm
FEC Events (Down/Up):
89364 / 1
CRC Events (Down/Up):
657 / 0
Loss of Framing (Local/Remote):
0 / 0
Loss of Signal (Local/Remote):
0 / 0
Loss of Power (Local/Remote):
0 / 0
Loss of Link (Remote):
0
HEC Errors (Down/Up):
9958 / 0
Error Seconds (Local/Remote):
0 / 0
Download speed at this time still 0.45 mps.
What is my next step to deal with this problem. Thanks!
P.S. I have gone through all the suggestions on the broadband connections sticky post - no new light shed by anything there. It did seem strange that for the speed check I always got that my details could not be found but I was able to continue anyway.

Answer 1

OK. 1) I've connected a shiny new ADSL filtre, 2) The wind and snow have long since stopped, so weather should not be an issue, 3) Yesterday the BT Service check page said there had been a broadband issue in my area but it had been fixed at 13:05 and today the service check so no problems. Since then my router has reset 3 times and I have had 0.45mbs rather than 4.5 for over 48 hours straight, a new record for me. As there anything else I can check/do before asking for a BT engineer to check it out. And what is the process for making that request?