Plug-and-Play (PnP) schemes represent a versatile approach that can be tailored to a wide range of imaging inverse problems. Considering the denoiser as the gradient step (GS) of a certain potential function, parametrized by means of a convolutional neural network, it is possible to determine the objective function which is minimized by the PnP iterative scheme. Based on this interpretation, we propose a block extension of a proximal heavy ball method with linesearch and evaluate its numerical effectiveness when the gradient step is performed by means of a GS denoiser. More in detail, we split the image into patches and use them as the blocks of our scheme. By doing so, the memory occupation for denoising is significantly reduced when performed on a single block. In addition, the convergence of the scheme is ensured under mild assumptions on the two terms composing the objective function. The experimental results confirm the effectiveness of the proposed block PnP method across multiple imaging problems, including deblurring and super-resolution, showing the reduced cost and time needed for each iteration. Furthermore, the proposed method allows to use PnP reconstruction techniques also in limited-memory scenarios, preserving both the convergence properties and the numerical performances.