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If at all possible run cable (Cat6) from where your router is to the back bedroom. Then buy a cheap POE switch and a couple of matching access points and connect it all up. That way your clients will connect to the nearest access point and not use the limited WiFi spectrum for backhaul. You can keep adding access points forever this way and cover any size house/garden. If you are feeling really fancy you can buy a waterproof outdoor access point and have brilliant signal in the garden.
If you can't run cable then you need some kind of mesh system which are a bit variable and need the access points to be close enough together to see each other so you perhaps need more. They should all match as I wouldn't trust them to interoperate.
Turn off the WiFi in your router.
Unifi needs a controller, I have them myself but if you aren't comfortable installing packages on Linux I wouldn't recommend them. The TP-Link Deco range seem popular here.
I've had a read of the thread but my sleep deprived brain can't figure out exactly what's best to extend my BT broadband so I get good signal the back bedroom and garden.
On my last deal I got the BT halo mesh discs thrown in but they don't really work. I've seen unifi ap mentioned, the look just like the BT halo discs but are they actually good? Do I just need to buy one and use with the BT router or do I need to buy a whole unifi ecosystem?
I'm sure I could figure it out but I'm very tired and looking to London's friendliest forum to just tell me what to buy.