The origin of the cross quarter days, as used by the Bricket Wood Coven, is indicated in The Stations of the Sun by Ronald Hutton as follows :-

"One of the 'Ulster Cycle' of early medieval Irish tales is 'Tochmarc Emire', the story of the wooing of Emer by the hero Cu Chulainn, which (at least in its extant form) was probably composed in the tenth or eleventh century. One of the tests which she set her semi-divine suitor was to go sleepless for a year, and in setting her challenge she named the main calendar points of the yearly cycle as they feature repeatedly in Irish literature of the time. Instead of denoting the cardinal points of the sun or the main Christian festivals, she indicated the opening of the four seasons."

The cross quarter days therefore appear to have been taken from Celtic myth which would help to explain the naming of the dates but I can't help feeling that it is rather odd for a group from the south east of England to have used this rather than Roman, Saxon, Angle or Norman. Celtic calendar information is very rare and the following is taken from the Wikipedia page about the Coligny calendar :-

"The Gaulish Coligny Calendar was found in Coligny, Ain, France near Lyon in 1897, along with the head of a bronze statue of a youthful male figure. It is a lunisolar calendar. It is now held at the Gallo-Roman Museum of Lyon."

"It was engraved on a bronze tablet, preserved in 73 fragments, that originally was approximately 5 feet (1.5 m) wide by 3.5 feet in height. Based on the style of lettering and the accompanying objects, it probably dates to the end of the 2nd century. It is written in Latin inscriptional capitals, and is in the Gaulish language. The restored tablet contains sixteen vertical columns, with 62 months distributed over five years."

In Wiccan literature I have often come across statements that Samhain marks the beginning of the Celtic year and yet from the same Wikipedia page we have the following :-

"the calendar year began with Samonios, which is usually assumed to correspond to Old Irish Samhain, giving an autumn start to the year. However, as Samon is Gaulish for summer (Lambert p.112), this assumed start is disputed. Le Contel and Verdier (1997) argue for a summer solstice start of the year. Monard (1999) argues for an autumn equinox start. Bonsing (2007) argues for a May beginning consistent with Irish Beltaine, and Fennian literature, notably Joyce (2000)."

If samhain was shown to be on any of the other dates it would have serious repercussions. Of course it could be that the Irish Celts used one date for the start of the year and the Gaulish Celts used another. The trouble with this idea is only that it would threaten the theory of the unity of the Pan Celtic world. The Coligny calendar throws up another interesting point which in this case is taken from the Roman Britain website :-

"Two of the main Celtic religious festivals Beltain and Lughnasadh were indicated on the Coligny calendar by small sigils, and each year started with the month of Samonios, during which period the festival of Samhain was celebrated. A fourth major festival Oimelc, which occurred during mid winter, is not indicated on the tablet."

This suggests that the time of year of Samhain is known on the calendar, at least in relation to Beltain and Lughnasadh, contrary to the debate suggested earlier. More important is the absence of Oimelc, or Imbolc, if it is supposed to be a major celebration. Imbolc is something of a mysterious celebration as there is virtually no historical evidence to support how it was celebrated. In The Stations of the Sun Ronald Hutton says :-

"It was placed in the Roman calendar, adopted by the Irish by the time that written records begin, on 1 February. The festival must be pre-Christian in origin, but there is absolutely no direct testimony as to its early nature, or concerning any rites which might have been employed then. There is, in fact, no sign that any of the medieval Irish writers who referred to it preserved a memory of them, and some evidence that they no longer understood the meaning of the name itself."