The answer to this question is "yes". The right to legal counsel upon arrest is a fundamental right in Canada and should you find yourself in such a situation, your first request should be to speak with a lawyer.
Under section 10(b) of the Canadian Charter of Rights and Freedoms, persons who have been arrested by the police have the right 'to retain and instruct counsel without delay and to be informed of that right'. In other words, the police are obliged to make clear to you that you can speak with a lawyer should you so desire.
Once you have exercised your right to speak with counsel, the police are duty-bound to assist you in contacting a lawyer at the earliest opportunity. You must be permitted to speak with your lawyer privately. You may also exercise your right to remain silent, whether you do so in the absence of counsel, or upon the advice of counsel.
If you do not wish to answer, politely let the officer/s know. Verbalising this makes it clear to all parties that you have chosen to exercise your right to remain silent, but it does not prevent the officer from asking you questions. However, if you have asked to speak with legal counsel, the police should wait until you have done so.
Obtaining legal counsel ensures you are given the best opportunity to understand not just your own rights, but also the rights the police can legally exercise. You have the right to continuously advise the police of your right to legal counsel and to provide suggestions on how you may be assisted with your request.
The content of this article is intended to provide a general guide to the subject matter. Specialist advice should be sought about your specific circumstances.