Multiresolution topology optimization (MTO) methods involve decoupling of the design and analysis discretizations, such that a high-resolution design can be obtained at relatively low analysis costs. Recent studies have shown that the MTO method can be approximately 3 and 30 times faster than the traditional topology optimization method for 2D and 3D problems, respectively. To further exploit the potential of decoupling analysis and design, we propose a dp-adaptive MTO method, which involves locally increasing/decreasing the shape function orders (p) and design resolution (d). The adaptive refinement/coarsening is performed using a composite refinement indicator which includes criteria based on analysis error, presence of intermediate densities as well as the occurrence of design artefacts referred to as QR-patterns. While standard MTO must rely on filtering to suppress QR-patterns, the proposed adaptive method ensures efficiently that these artefacts are suppressed in the final design, without sacrificing the design resolution. The applicability of the dp-adaptive MTO method is demonstrated on several 2D mechanical design problems. For all the cases, significant speed-ups in computational time are obtained. In particular for design problems involving low material volume fractions, speed-ups of up to a factor of 10 can be obtained over the conventional MTO method.