Line fault - clicking, recall & FTTC

[#1]

We have an intermittent fault, where we can hear clicks on the line occasionally. They have been fairly reminiscent of the kind of noise made by a recall button, and can come singly or in a short burst. They've not disturbed the call much (besides making you think the other person hung up), and never disturb the FTTC connection.
The nature of the calls means we were never certain which line had the fault - or indeed, if the fault was really part of the cordless phone/headsets.
Then today we had a call where the clicks were more annoying, and then happened to cause the actual behaviour of the recall button. That is:
- One person heard the "Please hold the line" message
- The other person heard, first, a message of "the number you have dialled has not been recognised", followed by "You will be reconnected to your call".
- Then we were reconnected.
This happened twice within 5 minutes or so - but then the clicks stopped, and haven't happened since today. It is very intermittent.
So the questions I have are:
- Am I right to believe that this now shows a line fault, rather than anything happening over the DECT portion?
- And that the faulty line belongs to the end that acted like they pressed the recall button, and heard the "The number you have dialled..." message?
- If the fault mimics the recall button, is it right that the fault is a break in the loop for a brief time (75ms or so)?
- Am I right to believe that, with no sign of disturbance to the FTTC connection, the break is likely to be somewhere on the E-side? Or could such a break, or click, or batch of clicks, fail to be noticeable to the modem?
Finally, is this kind of fault going to be detectable with a straightforward line test? Or do we need the line to be tested around the time the fault is actually occurring?
I'm wondering whether to put a ticket in now, or wait until the next time it happens...

[#2]

I'd wait until it happens again.
Were Openretch working at the (non-fibre) cab maybe (or even the exchange)? That could be causing it.
Which end of the call heard "the number you have dialled ........" message, your end or the other end? If it was the other end, it's likely it wasn't anything to do with your line, but I guess the way you've described things it was your end and as the fibre wasn't affected, it's highly probable it will be the 'E' side or at the exchange.

[#3]

The "the number you have dialled..." message was heard by my wife, on our fibre line. At the time, she was talking to me when I was elsewhere, and I heard the "Please hold the line" message. So yes - my assumption is that the problem was on our line (ie the one my wife was on).
We have no real way of knowing if OR were working in the cabinet at the time - we can't see the cab without a hike around the corner. We hear the clicks often enough to be unconvinced that this would be the cause - but I'll listen out & check in future, especially if they happen out-of-hours.
My wife reports that it wasn't wet, but it was starting to get windier (but not excessively so).

[#4]

Is it overhead cables on the 'E' side?
Daft thought - check your phone bill in case you have a crossed line or something 

[#5]

I'll check, but I don't think there are overhead cables on the E-side.
And a bill-check will be done tomorrow!

[#6]

We had more problems today, but adding symptoms that we get no dialtone, and the phone doesn't ring - and picking up the handset fails to answer an incoming call.
They're still intermittent though 
On the positive side, the bill doesn't look wrong!
I decided to raise a ticket: number 62236379.

[#7]

Sounds like an intermittent connection on the 'E' side. That was raised as a phone fault I take it.

[#8]

It was indeed. Quoted an 11 hour response time...