Phonology represents an important part of the English language; however, in the course of English language acquisition, it is rarely treated with proper attention. Connected speech is one of the aspects essential for successful communication, which comprises effective auditory perception and speech production. In this paper I explored phonemic assimilation, which results in successive sounds at word boundaries influencing each other, as an element of connected speech, and studied how teaching it can be supported with computer-assisted language learning. The research conducted revealed that elements of phonemic assimilation are found frequently in all styles of speech and thus, the knowledge of it is necessary for developing proper listening and speaking skills. I advocate the use of the Internet as one of the best possible resources of listening materials for learning phonemic variations and show how various web tools and means of technology can be used for preparing, presenting and storing educational materials. I believe this article makes a contribution to the corpus of research and instruction on connected speech as part of the standard British accent and will have an impact in raising general awareness of its significant role in the process of English language learning.