(For the context of this post, see the three previous posts.)
Yesterday evening, I received a further phone call from Zen, this time to arrange a time when an engineer could visit. We agreed a morning visit for the next day (today) in the morning. As is usual in such cases, they could say only that he would arrive between 8 am and 1 pm.
This morning, then, I rose bright and early to be ready by 8 am. Needless to say, the doorbell did not ring at 8 am or, indeed, for some time after that.
At 9:23 I received a text from Openreach: “Our engineer Joe [mobile number] has your job and will call you before working on your task [URL]”. The URL leads to a website with a diagram showing progress of the “task”:

As you can see, at that point it was standing only at “Engineer Allocated”.
At 10:29, the engineer rang to say he would arrive in about 20 minutes. He was right on time!
There then followed an hour during which the engineer performed tests and then made numerous phone calks to various agencies including Zen. This ended with him departing to the exchange to do some work there. He would then phone me to know whether I could now connect to the Internet. If so, the job would be complete; if not, he would have to come back here again.
Whatever the engineer did at the exchange did not produce the hoped-for result. At just after 1 pm he was back with me, saying that it was now thought there a problem with the router itself. After some more tests and attempts to obtain a result, done in consultation over the phone with Zen, work stopped as no further progress could be made today.
That of course leaves us without an Internet connection (apart from our iPhone hotspots) for another day. I received a call during the work from the Zen person, R, who called on Monday and he said he will call me again later today. Perhaps I can then discuss with him a way forward out of this apparent impasse.