They did not use an OS from Blackberry / RIM.
Vertu emerged from Nokia when they were at their peak - Frank Nuovo was the key designer there, and it was one of his projects.
From memory the original versions (Vertu Signature, Vertu Ascent, … ) used one of the Nokia feature-phone OSs as the base - maybe Series 30 or Series 40? - or they might have used one of the Symbian OS’es (Series 60).
They definitely used a Symbian OS in subsequent Vertu devices, before switching to Android later on.
They were incredibly well made devices, but ridiculous.
Source: I worked at Nokia for a while in a non-engineering role. I spent some time with a Vertu Ascent, and had access to the Vertu stores in Asia.