Using Time Capsule to extend a BT HomeHub I currently have a Time Capsule (5th generation mid-2013 tall one) and use it as my only WiFi and back up to it.

I am moving house and will be getting BT Infinity (Fibre), so I will get a BT HomeHub 5.  I will need to extend the range of the WiFi so it can reach all areas of the new house.

Can I change the config of the Time Capsule to be an extension of the HomeHub WiFi? I've read contradictory info as to whether the two are compatible.

If this is possible and I reconfigure my Time Capsule, will I have to restart my Time Machine backups from scratch again?  Currently I connect to the disk "Mark's Airport Time Capsule" which I assume will stay the same even if I reconfigure the WiFi connectivity?

EDIT: OR... would it be easier (and give better throughput) to use Powerline extenders to connect to the outlying room and then set up the Time Capsule &amp; HomeHub in a "roaming" network (i.e. both using the same SSID &amp; security) credentials)?
Answer to: 


  If this is possible and I reconfigure my Time Capsule, will I have to
  restart my Time Machine backups from scratch again?


Time Capsule settings and user stored data are separate things. You can erase the hard drive and keep the settings, and reset the settings while keeping your data.