In recent years, the phase field approach applied to crack propagation problems has gained in popularity in the scientific community. So much so that even if it was originally applied to brittle fracture, it was since extended to several other crack propagation mechanisms such as fatigue in Carrara et al. 2019. This is explained by the flexibility of the phase field model in a finite element framework in the context of crack propagation. However, these models usually suffer from prohibitive computing time. Consequently, in this work we put forward the coupling of two accelerating tools for phase field fatigue crack propagation simulations : adaptive mesh refinement (AMR) and a cycle jump scheme. A fatigue phase field model suffers from two major efficiency drawbacks. Firstly, the regularisation of the crack discontinuity on a small length scale means that a very fine mesh must be used. Thus, by coupling AMR and phase field, we can use a refined mesh only where it is necessary, yielding faster computation while keeping precision. In this work a refinement criterion based on the value of the phase field variable is used to achieve a flexible coupling between phase field and AMR. Secondly, the computation of a single cycle can lead to a high computing cost because of the high non-linearity of the damaged structure behaviour. Moreover, in the case of high cycle fatigue lifetime prediction, we must compute $N>10^5$ cycles. In this context, we use an implicit cycle jump scheme inspired by Loew et al. 2020 coupled to the previously described fatigue phase field AMR model. This iterative approach enables us to skip large number of cycles while keeping a predefined precision. To demonstrate the capabilities of the model, multiple benchmarks of the phase field fracture literature are first studied. We validate that the introduced AMR and cycle jump schemes yield precise and efficient results and couple them both to achieve maximum efficiency gains. After validating the coupling on mode I crack propagation, we demonstrate the ability of the model to recover more complex crack propagation patterns such as crack kinking, branching, nucleation and coalescence.