This paper introduces the contents and the possible usage of the DIRHA-ENGLISH multi-microphone corpus, recently realized under the EC DIRHA project. The reference scenario is a domestic environment equipped with a large number of microphones and microphone arrays distributed in space. The corpus is composed of both real and simulated material, and it includes 12 US and 12 UK English native speakers. Each speaker uttered different sets of phonetically-rich sentences, newspaper articles, conversational speech, keywords, and commands. From this material, a large set of 1-minute sequences was generated, which also includes typical domestic background noise as well as inter/intra-room reverberation effects. Dev and test sets were derived, which represent a very precious material for different studies on multi-microphone speech processing and distant-speech recognition. Various tasks and corresponding Kaldi recipes have already been developed. The paper reports a first set of baseline results obtained using different techniques, including Deep Neural Networks (DNN), aligned with the state-of-the-art at international level.