You seem to forget he is trying not to get caught, if guilty he would definitely have dialled 999 why not?
How can he assume it was a open and shut case, lots of things could have given him away, even walking / cycling with no lights he might still have been seen.
How can he assume it was a open and shut case
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Most criminals probably think that beforehand. Then they are caught. Bamber went on his first jolly up a couple of days after the massacre for goodness sake.
Bamber phoning the sixth furthest away police station is very damaging. He has never given a good reason.
Who an earth would receive such a call (at 3am), then think 'I must look for the number of my sixth furthest away police station'.