The broadband coming into your home is the same whether you are using wired or wireless (so BT cant do anythng to change it).
What makes it wireless is the device that is actually in your home that the PC or laptop connects to.
Most people have a MODEM in their house and the PC connects to that with a wire.
However you can replace the MODEM with a device called a ROUTER (that also has a modem inside it).
You can get WIRED routers (that only allow PCs or laptops to connect to them with a wire) or WIRELESS ROUTERS that allow PCs or laptops to connect with wires OR wirelessly.
So in simple terms you need to get a WIRELESS ROUTER (you may already have one, or BT may give you one free).
The great thing about a router is that you can have more than one device connected to it at the same time, so you could have your PC connected via a wire AND your laptop connected to it wirelessly and they can share the internet.
(Note you dont HAVE to use a laptop wirelessly, you can also connect laptop to a modem or router with a wire as well - same as your PC).