It gets worse ...
You have my sympathy. Seriously. Everything you describe below is entirely normal and typical of my experiences with Openreach on a regular basis. They're utterly unorganised and waste a huge amount of people's time and effort, and they couldn't give a damn.
The broadband activation is being held up as the phone line isn't installed yet.
They cant install the phone line as one of the poles they need to climb is rotten so they need the cherry picker to do that.
And what happens there is you play a game of waiting to see if one of the very few cherry pickers they have in your area will be free - because they're mostly booked "on demand" - but there is a great resistance to ordering assistance because requesting an "assist" gets you moaned at by your line managers, so some engineers do all they can to avoid even trying. If you get a Kelly or Quinn bod out, they'll just refuse to do the job and you won't even get a chance at the cherry picker game.
I wasnt on site but apparently the cherry picker turned up two weeks ago to do the work on that pole and the guys stood about for an hour and were heard to say "We'll just wait for the traffic lights" and left without doing anything.
Also normal - and unless they specifically requested an A55 you won't get any progress - they'll send someone else out eventually (when you chase basically) and the same failure will happen. And even if they just note that an A55 is required, nobody actually reads notes, so unless they go through to the right people, you get no progress. It takes forever to get them to do things properly.
It seems that I'm in this endless loop at Openreach.
You are. The same loop I'm in most weeks for a customer. Drives you absolutely insane. I've had upwards of 30 failed appointments for one customer alone because they can't read notes or simply lie - for example suggesting the customer refused access when in fact I was on-site an hour before them - they just didn't have the right people available.
i.e The broadband guys are waiting for phone line to be installed but the line isnt going to be installed as the cherry picker guys have decided they'll just wait until the broadband guys rock up with their traffic lights and do it at the same time. What a farce!
Not quite how it works - the engineer that installs the phone line cannot do so because he needs an assist (cherry picker bloke) - and quite possibly a groundsman too - unless the engineer is sufficiently trained and allowed (often not).
You also need Openreach to organise traffic management (this often means Lux or similar), which in turn may require an Openreach Survey. If the Openreach Survey is not actually very good (it generally isn't) you might find Lux are asked to supply say a two-way light set, but then they turn up and refuse to put the lights out because either a different setup is needed which they don't have and OR hadn't paid for, or OR didn't deal with things like road widths, and so Lux say on safety grounds they're not allowed to proceed. Then if you're really lucky you might eventually get a survey by lux, who then say what's actually required. Then you have to hope OR and Lux will co-ordinate a date.
When you get to that date, you might still find that they've not managed to organise that either, and Lux still refuse it because the OR van is too wide or some aspect wasn't done properly on either survey. If you're really lucky they might eventually negotiate a compromise and install the line.
...and once the line is finally in, you might be able to have broadband. Assuming the installed line has no faults.
Oh and this is a short version of a real world scenario I had just a month ago, that had been on-going for almost 18 months...
Nobody "broadband" is involved - it's all Openreach and it's sub-contractors like Lux (or whoever they use where you are) to get the thing done. Finally - depending on the location and road, you may also find OR need to give the council a nudge and submit a street works request.
All good fun... not!
Good luck!