The British WWI helmets are confusing because in the past Brodie and MkI were used interchangeability and now it is clear that there were multiple patterns.
There is the Type A - which Marcus Cotton said should be called the War Office Pattern Helmet. 20,000 helmet shells produced. Then there is the Type B, which is really the 1st Pattern Brodie. These are the ones with the raw edge. The MkI has the rimmed edge, but many of the early liners were apparently still marked "War Office Pattern," as that is the liner that is mostly seen in the Type A.
Cotton has been working on a book on British helmets that SHOULD clarify all this, but I don't know where the book is at this point. To add to the confusion J. Anthony Carter was also working on a book when he died in 2002 (which serve as a reminder to all wannabe writers... just publish already), and apparently some of Carter's work may have been based on Cotton's.