Which British computer scientist coined the term packet switching?

The British computer scientist who coined the term packet switching was Donald Davies.

Working at Britain's National Physical Laboratory, Davies recognized in 1965 that computer traffic was bursty rather than continuous like a traditional telephone call. He proposed breaking messages into short, standardized packets that could be routed independently and reassembled at their destination. He chose the word “packet” after consulting a linguist because it could be translated without losing its meaning.

Davies developed designs for high-speed switching nodes, now recognizable as routers, and proposed a national commercial data network in 1966. His NPL team built the first practical packet-switched local-area network: an early version operated in 1969, and the Mark I network became fully operational in January 1970.

Paul Baran independently developed a related packet-switching concept at RAND in the United States during the early 1960s, mainly with survivable voice communications in mind. That independent work explains why Baran is sometimes named in this question. Leonard Kleinrock made important contributions to queueing theory and network-performance analysis, but Davies is the canonical answer for coining the term itself. Davies's work also influenced ARPANET and later Internet networking.