Upgrading to fibre - basics

[#1]

Not decided yet whether to upgrade to fibre (depends very much on price, and whether I get to keep the existing £7.50 discount on the £9.99 current monthly payment).
If I do, though, I'm guessing it will mean:
1  A visit from an engineer to fit a new faceplate
2  A replacement router (presumably my long-serving Belkin will have to go?)
3  A new wi-fi extender (or will the existing extender continue to work?)
There's also a 20cm x 30cm plastic box on the wall, next to the existing faceplate.  There's a single cable feeding into it from the faceplate, and it distributes the internet connection throughout the house to a number of ethernet ports.  I'm guessing (hoping!) that box, and the connections into and out of it, won't need to be disturbed?

[#2]

I can answer some of it but not all
An engineer visit will be required and they may or may not fit a new filtered faceplate
A new router will be needed
Existing extender should work
But I don't understand you last point - where is your existing router fitted in the present setup

[#3]

Thanks for the reply.  I'm probably not expressing myself very clearly, but the router's connected to an ethernet port which is fed from the box on the wall next to the BT faceplate.

[#4]

Basically the new setup would probably be
Filtered faceplate with one phone socket and one fibre socket
The BT modem would connect to the fibre socket and a cable would feed from there to the router
I still don't understand this bit "There's a single cable feeding into it from the faceplate, and it distributes the internet connection throughout the house to a number of ethernet ports"
Where is the router in all this

[#5]

The router's connected to an ethernet port which is fed from the box on the wall next to the BT faceplate.  It could just as easily be connected to any one of the four ethernet ports across the house, theoretically.

[#6]

So you could connect the BT modem to the box and then pick the signal up from the port you are using with the router