"I had a chat with BT today, and it turns out the engineer is not coming any of those days, and will come at the end of the month "because they couldn't get access to the property". "
They tried this on me once. I offered to upload the CCTV footage showing they hadn't bothered turning up.
On another occasion the Openbletch tech parked outside for 25 minutes, then drove off, trying to claim "noone was home". CCTV footage showed that lie up too.