The answer to this question is undoubtedly, yes. The right to legal counsel upon arrest is a fundamental right in Canada and if you find yourself in such a situation you should always request to speak with a lawyer in the first instance.
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, police are obligated to make clear to you that you can speak with a lawyer, if you so wish.
If you have expressed your request to speak with a lawyer, the police have a duty to aid you in contacting a lawyer at the earliest opportunity and you must be permitted to speak with your lawyer privately. That said, a suspect also has the right to silence, a right to which a lawyer may advise in an attempt to avoid self-incrimination, as anything you do say may be used later as evidence. 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 by all means, it does not hinder 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 the rights the police can legally exercise. You have the right to continuously advise the police of your right to legal counsel and 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.