Something wrong

[#1]

An exchange issue would not cause other local WiFi routers to disappear from your laptop list. It could be some sort of wireless interference eg.microwave oven. Have you tried a different wireless channel? Is your wireless card drivers up-to-date?
When you say losing Internet and DSL, are either or both of those lights on the modem/router changing colour or flashing?
I can see there may be a possibility of the modem/router restarting, in which case it may be selecting a different wireless channel from previously and as your laptop changes to the new channel it will momentarily lose connection. When/if this happens next, log into the modem/router and look at the Event Logs (link for you, or goto >Technicolor Gateway >Event Logs) - and do a copy and paste of the content but redact the last octet of any Dst ip: address that appears ie. 87.115.42.xxx or whatever you have.
If this sort of thing is happening we'd be looking for Kernel Warm Restart or Kernel Cold Restart entries.

[#2]

Disappearing/reappearing WiFi signals may have been marginal signals, I don't know. I just wondered if I was not the only person in the area having router problems at the time.
Both the Internet was being lost and the DSL dropped as reported in the event logs. Kept on happening over and over again. Only as reported on the day, it has returned to normal since. No known environmental reason.

[#3]

So there were no Kernel Cold or Warm Restarts in the Event Log, just some xDSL linestate down and up and matching PPP link down and up?
I suppose it's possible that OpenReach were doing some work in your cabinet or the exchange, and it disturbed your connection.
The number of LoS in the stats should have increased by the same number of drops you had.
Did you notice them in the area? Is there a Fibre Cabinet in your locale being installed perhaps?
Another thought, is your line overhead or underground?

[#4]

I did a couple of router power off/on myself originally, it always seems the easiest.
But then looked at the router log when it kept happening. I had just turned the router's 'Webpage Interception' option from Automatic to Disabled at the time. But this seems just coincidence as I have turned it off again this evening and it is working. There is nothing to see now but hourly ntp updates and the usual occasional port scanning.
I haven't seen anyone working but I haven't been looking, and the line is underground.

[#5]

Yep, the Webpage Interception can be a bit of a pain in these circumstances.

[#6]

Something definitely wrong this morning!
Large 30% drop in download speed since starting router this morning. Several restarts managed to get it back up to acceptable 15,800kbps with a more normal 6.1dB SN margin.
But now dropped back down again to: 10,935kbps, 11 - 14 dB

[#7]

Are you checking regularly whether you can hear/have you heard any crackling or other noises on the line when using the phone? Have you had any problems with incoming or outgoing calls? Try the Quiet Line Test 17070 option 2 if need be.

[#8]

More drops than I'd like to see, especially today.
WBC 160K - 24M No delay (INP 0) 6dB Downstream, UC No delay (INP 0) 6dB Upstream (ADSL2+) - Not banded
Speed:  1187  15852 
SNR 6.0
Indicative Line Quality:  A 
Mean Time Between Errors Downstream (Seconds):  46 
Mean Time Between Retrains (Seconds):  86400 
The one I've made bold is the most concerning to me. Nothing else except the number of disconnections is too bad there.

[#9]

Most breaks are me disconnecting to try and reconnect at a higher speed.
Eventually succeeded after many tries and now at 15,852 kbps, 6 dB
As usual, on incoming calls I continue to hear intermittent crackles, fizzes and other noises. I don't generally make outgoing calls by landline, but whenever I test using BT Line Test and Quiet Line, I cannot hear any problem.

[#10]

Perhaps Chris could run a CLT for you just in case it shows up anything. Intermittent Line faults are a pain in the butt.

[#11]

I've just ran a line test 3 times on the phone line:
No fault was found after automated testing.
So if there is an issue causing the crackling, the testing isn't picking it up

[#12]

It's all gone 'Pete Tong'!
At 10.05pm the DSL dropped out again. Speed and NM up and down all over the place. I have changed the filter in use.
I keep seeing 'holes' appearing in the DSDstats Tones/Bitloading display. I wonder if my router is faulty, though it is a fairly new one.
I even had to redo this message off line as it dropped again while writing it, demanding yet another power reboot. Either my router is dying or BT's is.

[#13]

Dropped again! - reacquired ANOTHER new IP address...
30 Jul 2015 22:52:23 Recording started
30 Jul 2015 22:52:28 Timeout while retrieving stats
30 Jul 2015 22:52:28 No stats received
30 Jul 2015 22:53:28 Timeout while retrieving stats
30 Jul 2015 22:53:28 No stats received
30 Jul 2015 22:54:26 IP address is now 87.*.*.*
30 Jul 2015 22:55:28 Timeout while retrieving stats
30 Jul 2015 22:55:28 No stats received
30 Jul 2015 22:56:26 IP address is now 146.*.*.*
30 Jul 2015 22:57:25 Unable to login to modem/router
30 Jul 2015 22:58:25 Unable to login to modem/router
30 Jul 2015 22:59:26 IP address is now 146.*.*.*
30 Jul 2015 23:01:28 Timeout while retrieving stats
30 Jul 2015 23:01:28 No stats received
30 Jul 2015 23:02:25 Unable to login to modem/router
30 Jul 2015 23:03:09 Recording stopped
30 Jul 2015 23:03:12 Recording started
30 Jul 2015 23:03:36 Unable to determine IP address
30 Jul 2015 23:11:14 Unable to login to modem/router
30 Jul 2015 23:12:17 Timeout while retrieving stats
30 Jul 2015 23:12:17 No stats received
30 Jul 2015 23:13:15 IP address is now 37.*.*.*
30 Jul 2015 23:26:17 Timeout while retrieving stats
30 Jul 2015 23:26:17 No stats received
30 Jul 2015 23:27:15 IP address is now 83.*.*.*

[#14]

Do you have a Master Socket similar to the one on the left? Do all your Microfilters look similar to this?
Do you have any extension phone sockets, and what is normally plugged in where?

[#15]

There was noise this morning on 17070 - first time I have heard this for ages. So I can only conclude the line is subject to very sporadic bursts of noise.