Generative approaches have been recently shown to be effective for both Entity Disambiguation and Entity Linking (i.e., joint mention detection and disambiguation). However, the previously proposed autoregressive formulation for EL suffers from i) high computational cost due to a complex (deep) decoder, ii) non-parallelizable decoding that scales with the source sequence length, and iii) the need for training on a large amount of data. In this work, we propose a very efficient approach that parallelizes autoregressive linking across all potential mentions and relies on a shallow and efficient decoder. Moreover, we augment the generative objective with an extra discriminative component, i.e., a correction term which lets us directly optimize the generator's ranking. When taken together, these techniques tackle all the above issues: our model is >70 times faster and more accurate than the previous generative method, outperforming state-of-the-art approaches on the standard English dataset AIDA-CoNLL. Source code available at https://github.com/nicola-decao/efficient-autoregressive-EL