EG, if they start searching your car when they pull you over, and they don't have a warrant or you are not under arrest then the evidence collected is not admissible in court.
However the UK doesn't quite have a total "right to remain silent" law anymore, the current miranda warning is
"You do not have to say anything, but it may harm your defense if you do not mention, when questioned, something which you later rely on in court."
and as such taking the tact of not saying anything at all can actually get an innocent person into some legal difficulties if simply giving reasonable facts about your innocence would have helped the situation at the time of quesitoning.