There are many fascinating details about the case, as there are in many of the sensational nineteenth-century murder trials. (For those interested in mainly Victorian poisoning cases, I would recommend Katherine Watson's Poisoned Lives.)
However, I was a bit surprised by this:
Here is not just the first British serial killer – someone who has killed more than three people in a period greater than 30 days – but the first to exploit and abuse the anonymity of a new industrial age.
Going by this definition, I can think of at least one other case which preceded Cotton's spree and would meet the definition of 'serial murder' provided here: the well-known Burke and Hare murders.
Burke and Hare killed (at least) sixteen people over the period of a year (famously, for the purpose of selling their bodies to Edinburgh's corspse-hungry medical schools) and were hanged in 1829.
Furthermore, having recently reviewed a very worthwhile book on that case -- Lisa Rosner's The Anatomy Murders -- it was also apparent that the killers made great use of urban 'anonymity' to get away with their murders as long as they did.
In any case, I'm not sure that we'll ever know who the 'first' serial murderer in Britain (or anywhere else) was; in the end, we can only talk about the people who were caught.