The book you mention was published in 1982 - Tim Darvill published a more recent (and readily available) update called "Long Barrows of The Cotswolds" (2004 Tempus). There's a whole chapter on the history and classification of long barrow excavation and study, which points out that some of the old terminology (dolmens, passage graves, gallery graves) can be misleading. The book has various mentions of the use of timber in construction, including an interesting section on the construction of Wayland's Smithy, which may have started life as a timber shrine. A brief extract:

"Where chambers were made of timber the ends are usually represented archaeologically by substantial postholes that would have held half-section split tree trunks up to a metre in diameter. ... At Kings Play Down excavations in 1907 by Benjamin and Maud Cunnington revealed two large postholes, each 0.6m across and about 0.6m deep, which would have held the end posts of a chamber 4.5m long and perhaps a little over 1m wide. Turf had been packed around the sides of the box like structure to help support the walls. Whether the end-posts originally projected through the top of the mound cannot be determined, but it is certainly possible and this would have created a most striking ornament."

He also states:

"Where timber chambers were built ... the postholes found in excavation tell us nothing about the form of the timberwork that they held"

Good book, very readable, worth getting a copy if this is your interest.