So the problem has been solved. I did not try the PPPoE connection as I didn't need to in the end.
I got in contact with the IT company managing the internet connection in the office building I use. It turned out that another company in the building was having the same problem as me - specifically unable to connect to their VPN using a BT home broadband connection.
In the end there was a hardware fault at a third party location between my connection and my office.
The exact description (which is not very detailed) was "The issue was due to a faulty device in the datacentre and have temporally rerouted traffic until they can resolve."
In the end the issue was not at my end or BT at all.
Thank you for your help though I really appreciate it.