wifi in seperate office with sep electric circuit

I have 2 outbuildings both with their own separate electrical circuit, 1 outbuilding has phone line and BT router, the other outbuilding has a wired ethernet cable from outbuilding 1. A strong ethernet signal can be accessed but I am struggling with wifi. just purchased a Whole Home wifi BT gadget but this doesn't seem to pick up the disc from outbuilding 1. Any suggestions, is there not a gadget that I can plug into the ethernet cable which emits wifi?

A wireless access point e.g. https://amzn.to/2OUV5Te TP Link dual band access point £64

Lots of others available, so depends on budget but best to go for dual band devices.

Seconded, only buy dual band kit.

Thank you will give this a go.

If there's wired Ethernet between the two buildings why not attach the BT Whole WiFi Disks to that?

I have three in my house in which WiFi does not propagate well between rooms and they're all wired back to a cheap Ethernet switch.

I have a Fonera simpl router plugged on end of ethernet.