Make cycle awareness a core part of the driving test

Yep, sure does. I drive on the road every single day and don't see much good practice. And the drivers that have most recently passed their test are more likely to be in an accident which clearly means they are not following the good practice from their lessons and test.
If all drivers drove as if they were on their driving test how many accidents do you think would happen and how would they happen?

Let me be very clear - I don't think, and have never said, that 'everyday' driving is the same as 'driving test driving', and experience is just as important as education; however, there is also a very clear correlation between good education and good driving practice. Your assertion that pro-cyclist training is pointless because 'all practice goes out the window' is demonstrably false; a higher level of driver education leads to a better standard of driving - this has been proven statistically, regardless of your personal anecdotes. To put it another way - if 'all the practice goes out the window' then an untrained driver would be just as safe as a well-trained one!

The difference between UK and Sweden and Netherlands is that the risk of injury for cyclists is much higher here and the number of serious injuries is increasing.
In the Netherlands kids of about 11 have to do a practical and theory cycling exam in school. If the petition called for Bikeability level 3 as a prerequisite for a UK driving licence then high schools would be queuing up to provide it.

Absolutely - although experience is also a factor, this is more evidence that pro-cyclist driver education leads to safer conditions for cyclists.