I'm looking for something to access wi-fi without connecting to a telephone or broadband socket, or a router; something that I can connect to my tablet using an internet cable. I came across this on eBay: BT Home Hub 3.0 300 Mbps 10/100 Wireless N Router. Is this, or something like this, what I need?
That is a BT router and connects to a broadband phone line (and is also very old and obsolete).
What exactly is it you are trying to do?
The simplest way, providing you have a decent data allowance, is to use your mobile phone as a Wi-Fi hotspot, no cables required
You should consider getting a 4g broadband package which will come with a router that connects to the 4g network that you have opted to go with and you will be able to connect to that router with a wireless or a wired connection.
My phone can't do that, but thanks.
I'm happy with what I have, and would prefer not to switch, but thanks.
I want to connect to wi-fi without having to connect to my broadband or telephone sockets, or my router, because access to those is in a different area of my home.
Right, think I understand what you mean now. Have a look at these, they use your mains wiring to extend your broadband/WiFi
https://www.tp-link.com/uk/home-networking/powerline/tl-wpa4220-tkit/
I don't need an extender; I need something that works independently. But thanks.
I have no idea what you think you can use independently. You either need to connect to your broadband via whatever means or connect to a mobile signal.