Internet to an outbuilding

[CrouchingPeeky]

So as the title suggests, I need internet to an out building - well two to be precise. I have a summer house which I am turning into an office and an annexe at the bottom of the garden where my mother in law lives. As part of the electrical work to get power to the summer house/office I am getting the electrician to install cat 6 external cable from the main house to both out buildings. I very naively thought I could have a face plate on the wall and connect a router so I can get wifi in both. I gather it really isn't that simple. If I have internet hard wired to both buildings, is it possible to place wireless access points in each building? I have to say I've only just read about WAP so don't fully understand how they work and whether they are suitable.
For full disclosure, the summer house/office is 10 metres from the house and the annexe is about 50 metres. The reason I went straight to hard-wiring the cat 6 is because I will be working in the office, plus the distance from the house of the annexe I thought it made most sense for a reliable connection. My internet provider currently is Sky, so have their router but potentially moving to Zen soon if that matters

Thanks again

 

[CrouchingPeeky]

Both are going back to the main house and into the back of the router. Each will have their own port in the router

 

[CrouchingPeeky]

If the Plugged one of these into the Annexe connect ultimately to the main router via the Cat 6 external and whatever ethernet I need in the annexe, will this solve my problem?

https://www.amazon.co.uk/Sky-Q-Wireless-Booster-2020/dp/B08K3SXD6N/ref=pd_ci_mcx_mh_mcx_views_0?pd_rd_w=UABte&content-id=amzn1.sym.6aea875e-359f-49f3-864f-cff62d586b6a%3Aamzn1.symc.ca948091-a64d-450e-86d7-c161ca33337b&pf_rd_p=6aea875e-359f-49f3-864f-cff62d586b6a&pf_rd_r=1MCH8JGR0XA1Z97DFN0G&pd_rd_wg=Nt526&pd_rd_r=cdfa104f-0ade-4131-911f-dfbcafb4e61d&pd_rd_i=B08K3SXD6N