@neilnich01 

hey 

so if your internet is supplied by BT then you'll need to plug one tp link into the wall socket near the router then put the Ethernet in the tp link and the other end into your by router. 
 

the other tp link ( the one what emits the WiFi signal) you will need to plug in as close to your summer house as possible. 
 

if you have electrical sockets in your summer house and they're on the same ring main as the tp link you plugged into the router then it'll work fine. 
 

In regards to your Sky Q, the Q mesh only works with sky's routers so if you had a mini in the summer house it would still need to connect to another Q device and will not connect to your WiFi extender. However, if you're able to plug the extender in the summer house and there is an Ethernet port spare on the extender then put an Ethernet cable from that into your sky Q mini box also.