Shower Head in Bath?

My bath taps have a shower head attached to them - the connection is on the top side, in the middle of the taps.
Usually, I can push down a metal thing that switches the water from taps to shower head, but it's not working. The water comes partly from the shower head (mainly actually) and partly from the taps and whatever I do, it will not change.
My question is, can i unscrew the connection at the top of the taps (the pipe to the shower head screws off no problem but water just comes out of the top of the taps instead!), and if so, how. And what do I need to do to fix it once I have removed it?

Many Thanks
Adam