Based on my experience, the door close button seems to work as expected at my office. Press the button, and the doors close much more quickly than they usually do.

As for crossing buttons... generally they do work in the UK. It's just that if the crossing is in the middle of a normal road (read, where there's no reason for the lights to change automatically) it's required, whereas if the crossing is at a junction, it'll merely display the signal to cross whenever the lights would be set to change anyway.