The purpose of 31st British Colloquium of Theoretical Computer Science BCTCS2015 is to provide a forum in which researchers in theoretical computer science can meet, present research findings, and discuss developments in the field. It also aims to provide an environment in which PhD students can gain experience in presenting their work, and benefit from contact with established researchers. The scope of the colloquium includes all aspects of theoretical computer science, including automata theory, algorithms, complexity theory, semantics, formal methods, concurrency, types, languages and logics. Both computer scientists and mathematicians are welcome to attend, as are participants from outside of the UK.