Why give the address and workplace to the police? Maybe when he gave his name he didn’t appreciate that he would have to give extra details and then judged it sensible to give a true address and workplace in case they checked. If he gave false details and they checked it would be worse for him as they would then actively search for him and he would come under suspicion. I would suggest it was a calculated risk – and using the name Cross was enough to murky waters yet not enough to get him in total trouble if found out.
Its looks very much like Paul , who was walking quickly and in poor lighting was already in the process of passing CrossMere and the murdered Polly ..
So ... Danger passed ? Why then would CrossMere, murder weapon in possession and blood possibly still on his hands tap Paul on the shoulder and draw his attention back across the road ( unless his main objective was to incriminate paul further by wiping the blood off his hands and onto Pauls coat

Another piece of this ill fitting jigsaw is the fact that it was Paul who pulled down her clothing to cover her modesty . If we are to believe that it was CrossMere who hatched this whole abort routine and subsequent escape plan then you would think that it would be he, who would have pulled her clothing down as soon as he became aware of the approaching paul. It would make it a lot easier to excuse her as just a drunk sleeping it off . And both men could go about their buisness . No drama .
cheers
moonbegger
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