Bryant & May Strange Tide by Christopher Fowler

Dry wit and charm aside, Detectives Bryant and May are part of a less than stellar, quirky London agency called the PCU - Peculiar Crimes Unit.  When left to their own devices they have successfully solved a fair amount of crimes but now John May is working overtime because his long time partner, Arthur Bryant is slowly slipping into dementia.  Even though Bryant has been told to stay home, he doggedly works on solving their newest case - a young woman who has chained to a post and left to drown in the Thames.  Half the time Bryant is busy combing the streets of London looking for clues but the problem is that he is usually not aware of what century he is in and his mental time traveling is getting to be difficult to hide.  His partner must try to keep Bryant hidden, upright and solve the murder.  This is one of a series but you don't need to read the others to enjoy the high jinks of this modern day Sherlock and Dr. Watson combo.