I think. It's been a while since I looked at the strict policy and regular interpretations. Police don't have to wait for a solicitor though, that's up to you and you have to ask for one straight off. If you're in the UK and you are arrested, be very polite with them, ask for a solicitor and wait, even if you know you're innocent. Actually, especially if you know you're innocent.
But should you choose to use your own solicitor, it may adversely harm your defense, because innocent people use the duty solicitor...