This morning's commute and other commuting stories

^^ I read somewhere that cyclists don't have to wait until the person has completely cleared the crossing but just "give way".
You're possibly thinking of zebra crossings, where there are no lights, and vehicles (including bicycles) must give way (or more explicitly, "accord precendence") to pedestrians that are already on the crossing.

On a bicycle you are a vehicle and the rules apply to vehicles.

In theory you could dismount, walk through the pedestrian crossing and remount on the other side, however, in most instances where this would be a viable option, you could open yourself to a charge of obstruction of the highway.
It does depend, of course, on what the lights are doing. Flashing amber, for example, means give way at the line, while red means do not cross the line.

I doubt that anyone has ever been pipped for obstruction of a highway for walking through a set of lights - given that there is no obstruction going on.