I have attended to 3 different interviewing procedures for Dyson. In all of them there was a first contact with the recruiter in charge of the position, once that it is everything clear, if positive, they will arrange you a first interview with the technical manager in order to speak about the technical details. If moving forward, the manager will give positive feedback to the HR people and they will schedule a longer technical interview with the area managers in order to evaluate your capabilities.
In that stage, I have encountered 2 different ways, but all of them had in common that you will be presented with an exploited/section image of a Dyson product and you will be asked to speak about it and describe with as much technical details as possible, what you could guess about every piece and its functions. Then, in one of them I was asked to develop a little technical exercise in which they evaluate your approaches to the problem to be solved and how. And in the other ones I was just asked about my previous expertise regarding different technical aspects and to provide reasons to sustain my decision.