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Just getting the Unifi UAP-AC-LITE will make the biggest difference and it's pretty affordable and will survive many ISP and router changes.
You can always get a second access point, but you will have to run cable for it and do the setup dance yourself.
If you're feeling spendy I'd consider the Ubiquiti Amplifi solution now too:
- https://store.amplifi.com/products/amplifi-mesh-system
- https://www.amazon.co.uk/Ubiquiti-Amplifi-System-Wireless-router/dp/B01L9O08PW/
I recommended that to someone living in a cottage and whose walls made WiFi so bad that the they ended up trying to install 5 different WiFi access points. It was fully replaced by this solution and it worked really well (key point: they didn't need my help setting it up).
- https://store.amplifi.com/products/amplifi-mesh-system
I bought a Ubiquiti UniFi UAP-AC-LITE access point based on the advice @Velocio gave and it's amazing. Rock solid Wi-Fi, no problem with a dozen things being connected to it. This one:
https://www.amazon.co.uk/Ubiquiti-Networks-UAP-AC-LITE-Access-Point/dp/B016K4GQVG
I didn't bother getting a UniFi router, I'm just using my ISP's. Wi-Fi is super fast, totally reliable and there's a good signal all around our flat as well as in it. Wouldn't go back...