Is it possible to put under arrest individuals who went to an escort and had sexual intercourse a week ago?

I was checking whether an individual visited an escort and engaged in a sexual encounter a week or so ago. Is the police still able to prosecute? I wondered whether you was going to be arrested or not would not the police arrest you on the spot? What will it be when you receive a phone call made to you by that escort a week later and it only rings a few times and drops?