Useless call centre - how can I get an intelligent...

Question

My broadband is dropping every couple of days, often for 5 to 10 minutes.  Red lights on the modem and the BT Home Hub  splash screen on the computer saying it can't connect to the internet.
I phoned the help number and spoke to a call centre presumably in India judging by the accent and odd use of the english language. 
He checked the connection at his end and said it was fine.  I repeated that it was OK now, but it had dropped an hour earlier, well as every couple of days.
"Now I have to explain something to you sir.  Your hub can accumulate blockages.  It is like static electricity they can make your light turn red and block your connection."   WTF?  He asked me to reset the hub to get rid of the static, despite the fact that I'd told him I pull the power on the hub every couple of days in the vain hope it'll speed up the reconnection (it doesn't). 
Then he said again that his computer says there is no problem with the network so the fault must be in my house.  So I repeat that the problem took place an hour ago, so the connection is fine now.  I asked if the dropped connection an hour ago showed on his computer.  "No sir. I can see your connection is fine". I asked about dropped connections in recent days, but  he said there had been no dropepd connections.
He then started talking about wifi settings and that lots of devices on wifi can cause problems.  So I repeated again that the box has a red light and all my devices can see the homehub interface, but we cannot get connected to the internet.
Then he started on about making sure we have the right wifi channel.  So I said I wasn't going to talk about wifi anymore, the problem is with the network, and it happened an hour ago, and it happened on other days.  "No sir, your connection is fine, I will email you some details about how to improve wifi in your house."
I then said I didn't want to talk about this anymore and I would end the conversation. I put the phone down.
Then my mobile rung "Sir, I have to tell you about your wifi."  I reply "No thank you, I don't want to discuss this with you"
Then my moble rang again "Sir, there are some things I can tell you about fixing your wifi."  I reply "No thank you, I don't want to discuss this with you"
arrrrggggghhhhhh !
Is there any way of speaking to a person who understands that a red light on the modem and a homehub that says it is dicsonnected from the broadband might actually be a problem with the broadband connection? 
Also when I've had the same thing a few years ago I though the helpdesk operator could see how many dropped connections had taken place?  The chap tonight was insistent there was no record of dropped connections.
edit to add:  I'm on a Hub 5 type A plugged into the master socket.  No other sockets in the house.

Answer 1

1. Product name:
BT Home Hub
2. Serial number:
+068343+NQ34940784
3. Firmware version:
Software version 4.7.5.1.83.8.204 (Type A) Last updated 22/01/15
4. Board version:
BT Hub 5A
5. DSL uptime:
0 days, 00:58:41
6. Data rate:
9995 / 39993
7. Maximum data rate:
11929 / 48683
8. Noise margin:
6.6 / 9.5
9. Line attenuation:
25.6 / 20.4
10. Signal attenuation:
25.4 / 20.0
11. Data sent/received:
8.6 MB / 61.5 MB
12. Broadband username:
[email protected]
13. BT Wi-fi:
Yes