You're right that the charter does contain a specific right to counsel, but the right to publicly funded counsel is really a matter of judge-made law. I think it's under the charter right to full answer and defence, but I haven't read the case in many years. It's a fairly old decision. It's known as Regina v. Rowbotham, a case in Ontario involving one of Ontario's most famous drug traffickers, actually, Rosie Rowbotham. There were a bunch of them charged. This was very a long trial. It was a conspiracy charge, and there were a couple that couldn't afford their own counsel but were not considered eligible for legal aid under the financial eligibility criteria. The court improvised a remedy, which was to order a stay of proceedings unless the Crown provided for a publicly funded defence counsel.
Rowbotham applications are frequently brought in courts across the country, and orders are frequently made.