Atually Naro the shooting scenario is a quote from massad ayoob the US gun writer.
But i appreciate what you say. our caution on arrest goes:

'You do not have to say anything. But it may harm your defence if you do not mention when questioned something which you later rely on in court. Anything you do say may be given in evidence.'

So you could go to court with 6 people providing an alibi
and the judge (note not the prosection; the judge!) will be pointing out you sat in a police station for a week without telling them you had an alibi and now suddenly when
you have had the opportunity to brief them they turn up. And they should regard that as an indication of guilt.

Maybe you have a right to silence that can't be used against you.
But as OBG says when it's a simple matter of explaning why not talk?
The Sock