Request DLM Reset
The engineers had reported back to advise they've tested the line and aren't showing any issues so they're wanting to test the line from inside your property although I appreciate that's already been checked before.
With the limited information we've received from the engineer and the escalation team it'd be difficult to advise why the engineer hasn't checked the underground wiring or if indeed this has already been checked and not documented.
At this stage, I think it's going to be a bit fruitless booking another engineer appointment without arranging this with you first as it seems clear they're wanting access to investigate further and while I can't 100% guarantee what steps will be taken on the day of the visit or we won't need to arrange a further visit I'll make sure we keep this escalated as much as we can.
I'll hang fire on that actually, following my last post I received an email from the escalation team to advise they've highlighted this to the 'patch manager' and while I've booked the engineer for Tuesday afternoon to keep the fault open on the Openreach system I'm asking whether they'd still be able to try to get this investigated externally.
I should know more by the close of play tomorrow with regards to whether we'd need you (or somebody) to be home.
Sorry for the hassle and frustration.
Based on the email I sent before I got that reply, which queried the reasons why the engineer didn't carry out the underground work, I'd suspect they've highlighted that to the patch manager.
I've since emailed to ask whether the appointment I've been asked to book for next week will be for an engineer to visit you or whether they'd still be able to try to get this sorted externally.
Hi Mat,
I got an email back not long ago to advise they've left notes for the engineer to call us on the day before visiting you and they've also emailed the field operations manager again.
Seems to be the same steps that were taken previously so I'm not confident the engineer won't need access to investigate further. 
If you can I'd book the Tuesday afternoon off work. Sorry again for the hassle.
Hi Mat, they've not said that in so many words but any escalation we raise is to ensure a full investigation is carried out.
While there's an open fault in the Openreach system, line tests come back with "Test Rejected" but I've checked BT's Reactive Repair Tool(RRT) data accurate as of yesterday and that's showing your sync speed has indeed increased to 64.4mbps
I've given the profile on your account a poke to reflect this, it should update automatically to match a sync speed/IP profile of the line but occasionally it can take a few days to do this by itself.
Can you disconnect and reconnect your router? You should see a higher download speed afterwards. We've nothing back from the engineer yet, feel free to let me know how it goes once they've arrived and/or have been.