@RobMob123
Thank you for posting on the TP-Link Community.
a) allows me to turn off devices/all devices via an app.
Kevin_Z: Mostly all the Archer VDSL modem can support this, you may check this guide, and see if it matches your requirement: https://www.tp-link.com/support/faq/2584/.
b) This is devices connected via wifi or via an ethernet cable plugged into a TP link powerline.
Kevin_Z: The modem should be plugged into the DSL line directly when working as a DSL modem router, it can be plugged into a powerline adapter with an Ethernet cable when working as wireless router mode. The models with a WAN port can achieve this, such as Archer VR2100: https://www.tp-link.com/home-networking/dsl-modem-router/archer-vr2100/#specifications
c) This needs to be timer configurable. Eg. turns of at night automatically.
Kevin_Z: The models with Wireless Schedule feature should support this, such as Archer VR2100:
d) The speed of the data on the modem only needs to match the basic EE modem provided by them
e) and be compatible with them: “Routers supporting Ethernet WAN (you might hear these called Ethernet or cable routers) can be used to connect to our Fibre Broadband service.”
Kevin_Z: All the models should be compatible with EE internet, you may check what is the bandwidth you got from them, then choose the approprete model:
https://www.tp-link.com/home-networking/dsl-modem-router/
Hopefully, that answers your question but let us know if you need more details.