i am with BT broadband. if i install WI FI do I still need a Router ?

If you are with BT Broadband, they provide a router, which they call a BT Home Hub or BT Smart Hub as part of their service.

For ADSL broadband services, any of the BT Home Hubs are suitable.All the Home Hubs include an ADSL integrated modem. For BT Infinity, you need a Home Hub 3, 4 or 5 or the new BT Smart Hub. With Infinity, you will be provided with a separate modem if you have a Home Hub 3 or 4. Home Hubs 1 and 2 cannot be used with the infinity service.

It is the Home Hub or Smart Hub that provides the WiFi signal that your WiFi devices will be connecting to in order to access your Internet connection.

So, YES, you need a router, but BT provide this as part of the package. Effectively you rent this as part of the minimum contract period, after which it is yours to keep if you subsequently leave BT's broadband service. Apart from the Home Hub 4r, which was in limited production, BT routers are locked to work only with BT services while acting as routers. You can use them as wireless access points with other ISPs.

I hope this helps.

the router is what should already be giving you a WiFi signal.

you need the router/modem to connect to the internet, so yes, you still need it.

The router provides the wifi.

yes