Disconnects and Low download speed

Question

We've had BT Broadband for over 10 years.  We had a few problems at the start and had to stop using any of the telephone extensions when it was installed to get it working.  Since then we've invested in numerous filters in an attempt to cure connection drops and bought an i-plate when the speed was suffering.  Every so often, I get fed up with the time it takes me to deal with connection drops and ring the call centre. They are very sweet but all I get is a temporary solution at best and then it all goes poof again.
For the last year or two so resetting everything and waiting hasn't always been good enough to get a connection again.  By accident, I found that if I made a telephone call, the broadband would come back again without me having to reset.  This proved an expensive option until I discovered the quiet line test (for which I thank the helpful members here lol). My trouble is that its taking quite a long phone call to get the connection going now and it used to be worse when it rained but its now as bad if its sunny.
A possibly related issue is that our download speed has declined enormously over the years.  I've not been able to watch the iPlayer since last year sometime and even YouTube pauses for ages every 10 seconds.  i've had two Openreach engineers out recently and there is another fault report in progress atm.  The trouble is, they don't seem to have made much difference so I'm despairing at the thought of another fruitless visit now.
My 'stats' are:
1. Best Effort Test:  -provides background information.
Download  Speed
0.47 Mbps
0 Mbps
0.5 Mbps
Max Achievable Speed
 Download speedachieved during the test was - 0.47 Mbps
 For your connection, the acceptable range of speeds is 0.1 Mbps-0.5 Mbps.
 IP Profile for your line is - 0.5 Mbps
2. Upstream Test:  -provides background information.
Upload Speed
0.96 Mbps
0 Mbps
0.83 Mbps
Max Achievable Speed
Upload speed achieved during the test was - 0.96Mbps
 Additional Information:
 Upstream Rate IP profile on your line is - 0.83 Mbps
We were unable to identify any performance problem with your service at this time.
It is possible that any problem you are currently, or had previously experienced may have been caused by traffic congestion on the Internet or by the server you were accessing responding slowly.
If you continue to encounter a problem with a specific server, please contact the administrator of that server in the first instance.
ADSL Line Status
Connection Information
Line state:
Connected
Connection time:
0 days, 00:02:03
Downstream:
568.3 Kbps
Upstream:
1.062 Mbps
ADSL Settings
VPI/VCI:
0/38
Type:
PPPoA
Modulation:
G.992.3 Annex A
Latency type:
Interleaved
Noise margin (Down/Up):
25.6 dB / 6.1 dB
Line attenuation (Down/Up):
44.6 dB / 26.9 dB
Output power (Down/Up):
15.5 dBm / 12.2 dBm
FEC Events (Down/Up):
0 / 0
CRC Events (Down/Up):
0 / 185
Loss of Framing (Local/Remote):
0 / 0
Loss of Signal (Local/Remote):
0 / 0
Loss of Power (Local/Remote):
0 / 0
HEC Events (Down/Up):
0 / 1238
Error Seconds (Local/Remote):
59088 / 4962
I've been reading about resistance faults and wondered if our ancient telephone lines round here could be causing one?  We're still on overhead lines I'm afraid and nearly 2km from the Batley exchange.

Answer 1

Just a quick update this morning.  I emailed the mods yesterday so I have hopes.
On the 'normal route' side, the phone call from BT techies that the call centre booked me in for between 8am and 10am didn't happen and there was nothing updated on the online fault progress report since the call centre folk updated it yesterday.  I rang the call centre again to tell them it hadn't happened so they are in the loop and its been escalated again. Had to go through their standard script etc but, hey, I'm reconciled...
The router stats today are:
ADSL Line Status
Connection Information
Line state:
Connected
Connection time:
0 days, 01:09:50
Downstream:
574.3 Kbps
Upstream:
1.059 Mbps
ADSL Settings
VPI/VCI:
0/38
Type:
PPPoA
Modulation:
G.992.3 Annex A
Latency type:
Interleaved
Noise margin (Down/Up):
8.7 dB / 6.0 dB
Line attenuation (Down/Up):
44.5 dB / 26.8 dB
Output power (Down/Up):
16.7 dBm / 12.6 dBm
FEC Events (Down/Up):
71 / 109
CRC Events (Down/Up):
0 / 45
Loss of Framing (Local/Remote):
0 / 0
Loss of Signal (Local/Remote):
0 / 0
Loss of Power (Local/Remote):
0 / 0
HEC Events (Down/Up):
0 / 27
Error Seconds (Local/Remote):
8 / 33
The noise margin has changed (it was 6 dB when I looked at it first  thing this morning in preparation for my phone call so I presume someone has adjusted it?  The speed test is coming up with the same figures as before and I can't post it because I forgot to copy it and now I'm getting apache errors.