Or he could have been 70% sure he didn't need to phone his cottage from WHF. So didn't.
He got lucky.
Either he knew the calls could not be traced, or he suspected they could Adam, but either way your scenario does not work.
If he knew the calls were traceable then he is tied to a impossibly tight time frame, and if he knew the calls could not be traced then he either dials 999 or the police direct and says "my father called a few minutes ago"
I thought you were going to submit a plausible JB scenario that answered all this?