My experiences of BT Infinity 2 and BT in general have been just as poor, I'm afraid.
Originally, I had the Hub 3.
I was sharing the property with a friend, James and the account was in his name. After a few days of enjoying 60-70 mb the speed dropped to a steady connection at around 50 mb. Ok, not as fast as we'd hoped but still very fast.
Then we started getting the odd drop out where the connection would cut out completely and several times a day the speed would drop to 20, 10 or even 2 mb.
We went through all of the things you have described and it took an engineer visit before BT would believe that it wasn't just the wireless connection that was the issue.
The second time we had an engineer out he said that the Hub 3 was "cr*p" and he would ask them to send out a Hub 5.
This never came.
By the time James moved out our contract was almost up so, believing the engineer that it would be far better with a Hub 5, I took over the line in my own name, started a new contract and a Hub 5 arrived.
To cut the story shorter, the above process has happened all over again.
We've also had to start the investigation process all over again because they will only recognise the start of the complaint as being when my girlfriend complained and not when James originally complained.
We have to take time off work for engineer visits becasue they only work during the day Mon - Fri but after two visits we're no closer to getting this solved. In fact the first engineer basically said there was no problem and the second was convinced that he had solved it. On that second visit he ran a speed test and it had dropped to 1mb. He switched us to another line, ran a test then went away happy that it was solved.
He'd been gone less than an hour before our connection dropped out again.
In total we must have been on Infinity 2 for, maybe 30 months at around £44 / month. That's over £1300 paid out for a pathetically slow connection, poor customer service and engineers who will only turn up when we're at work.
We've asked if we can be released from the contract but no, we have to continue paying full whack and putting up with this shambles.
I've every sympathy for you, mtrav and wouldnever recommend BT to anybody.
I moved your post so replies will be about your problem and not the other thread originator
as with other thread can you post the stats from your hh5 by going to troubleshooting then helpdesk and post 1-12
can you enter your phone number and post results remember to delete number https://www.btwholesale.com/includes/adsl/main.html
are you using the test socket or do you have a SSFP
if you post the information the forum members will try and help and failing that the forum mods can help - they are only BT employees on the forum