To the OP, looks like that's a trunk road junction, if you want to air your concerns, suggest using HAIL, via
http://www.highways.gov.uk/about-us/contact-us/?hc_location=ufiYou should get a holding response back and eventually a response addressing your query - that might or might not answer your questions!
Given it's a motorway/trunk road junction, I would suspect priority (rightly) is for ensuring clear passage of traffic on and off the motorway network and it will aim provide a safe crossing whilst managing the traffic, but its priority will be the traffic. At a slot in time, the green man will invite the pedestrian to cross if they view it safe to do so and a calculated time for them to cross will be used, on streetview you can see the on-crossing detectors (little black boxes on the poles pointing at the crossing area), these will be used to sense that the ped is still crossing and extend that time if required.
In some places peds are given more priority than vehicles, there are some signals in our city which are actually ped crossing all the time and the vehicles have to wait to be serviced. Its a balance between all road users and also the specific needs of the time of day (priority to main routes out of town between 16:00 - 18:00 for example)
The reason why the ped crossing phase isnt instant is that the traffic signal controller is running through a cycle, which might be controlled through a number of different ways with the various set of lights being called by demand (count of cars say) or a timetable. When you press the button, it's a bit like putting your hand up in class, the teacher will get round to you eventually, but if there is some higher priority to deal with you'll have to wait for a slot. Sometimes there is a ped waiting detector to help ensure that if the ped has crossed before the green invitation to cross that teh demand for the pedestrian phase is skipped.
In terms of cycles and triggering lights. There are a number of detectors that can be used, the worst for cycles is probably magnetometers (detecting the impact on the earths magnetic field by a vehicle) the most common are inductive loops in the road. You can help yourself be detected by 'shorting the loop', i.e. placing your bike in a position that has the greatest effect on the inductive properties of the loop. In plain english, ride along the black slot in the road that is the end of the loops, i.e. the bits parallel to the kerb... note some loops do different things (detect queue, clear queue etc) so if in doubt, hit them all up to the stop line!
The above is all very generic but hopefully answers some of the questions and myth in the thread. Plenty more info on the web but without knowing a significant amount of detail about specific sites i.e. the location, control strategy and the reasons behind it, you will always be guessing why it does what it does - signals in Essex for example work differently to signals in London, which all work differently to say signals that are on motorway interfaces... then sometimes they all work the same - you can't fully tell just by what is visible and remember your interpretation of timings etc is just valid for the snapshot you witness it - without knowing the configuration of the actual site, you don't know if it was under remote control, local control, demand driven or timetabled.... or worse still - the detectors are faulty and therefore the expected behaviour is not what is been seen.... the only persons who probably stand a chance in being able to decipher all that would be a Traffic Signal Engineer, which I am happily not one LOL!