We have put together a short survey to capture your feedback in terms of what BT can do when you experience home Wi-Fi issues. We would appreciate it if you could take a couple of minutes to complete a short survey. Read more from here, Fix my home Wi-Fi
It may take some time. BT can probably restore your telephone service without needing access to your premises but they will need to revisit to install the new modem that Infinity requires (if that was not done previously).
I marvel at BT's ability to sell its more expensive products on the back of less expensive ones not working properly. Quite a few problems that have an adverse effect on ADSL broadband also have an adverse effect on VDSL ("Infinity").