Single-channel speech enhancement algorithms have seen great improvements over the past few years. Despite these improvements, they still lack the efficiency of the auditory system in extracting attended auditory information in the presence of competing speakers. Recently, it has been shown that the attended auditory information can be decoded from the brain activity of the listener. In this paper, we propose two novel deep learning methods referred to as the Brain Enhanced Speech Denoiser (BESD) and the U-shaped Brain Enhanced Speech Denoiser (U-BESD) respectively, that take advantage of this fact to denoise a multi-talker speech mixture. We use a Feature-wise Linear Modulation (FiLM) between the brain activity and the sound mixture, to better extract the features of the attended speaker to perform speech enhancement. We show, using electroencephalography (EEG) signals recorded from the listener, that U-BESD outperforms a current autoencoder approach in enhancing a speech mixture as well as a speech separation approach that uses brain activity. Moreover, we show that both BESD and U-BESD successfully extract the attended speaker without any prior information about this speaker. This makes both algorithms great candidates for realistic applications where no prior information about the attended speaker is available, such as hearing aids, cellphones, or noise cancelling headphones. All procedures were performed in accordance with the Declaration of Helsinki and were approved by the Ethics Committees of the School of Psychology at Trinity College Dublin, and the Health Sciences Faculty at Trinity College Dublin.