Boosey &Hawkes shells, changed around over the years, a bit, so from photographs it is difficult to tell but I think it is an Ajax. I don't think they made an Edgware or Besson narrow drum. Based on the badge shadow, it looks like Grantro is offering you the right badge. Most of the shells were Birch. I can't get at the parts, right now, to determine the dimensions on all the holes but I do have a throwoff and lugs, handy and the holes for those should be 1 11/16'' and 1 1/4" between them, respectively.
The lugs for the Pipperette are different than the standard Ajax bullet shaped lugs, that were used for so many years. They fit the same holes and are in all ways the same , except that the ends are clipped off, in order to fit the narrower shell. They may be difficult to find.