Hi Al,
my first/immediate thought is that "Drybrook Chapel" refers to Holy Trinity Church, above Drybrook on Harrow/Harry Hill, as thats the nearest CoE Church, also known as Forest Church.
Some more info here
http://forest-of-dean.net/index.php/component/content/article/8-pages/103-about-the-forest

I say this as I wonder if you, like others before you including me, have assumed that where the PR says "Chapel" then you're thinking just small Chapels rather than more typical "larger" Churches ?; whereas in fact all the site's PRs use the word Chapel as a generic term irrespective of whether the actual place a PR refers to is a CoE Church, or a Baptist Chapel, or whatever.

That said, there were some non Conformist Chapels in the area, of course, including on top of Plump Hill towards Harrow Hill & Drybrook. This extensive hostory of the area includes several mentions of Drybrook and it's various Chapels.
http://www.british-history.ac.uk/vch/glos/vol5/pp396-404

Normally I'd expect to see some clues to such a background within a person's history, such as place of marriage etc, otherwise I'd assume it to be Conformist CoE. I've found that some Chapels didn't/don't have their own Burial grounds, unlike Holy Trinity. Also some Chapels were only in existence/use at certain times, possibly not when this Burial took place, whereas Holy Trinity was the first CoE Church within this eastern side of the Forest and is still in use today (sorry for perhaps stating what you know, I don't know how well you know the area).

Another clue I guess is the Minister's name, which hopefully can be searched and tied to a particular religion ? In this instance entering William Barker into this site's general search box gives the following hit.
It's perhaps not as clearly labelled as it could be, but the resulting page is from the Kelly's Directory for 1879, and states

"[HOLY TRINITY.] The church, which is 4 miles south from Mitcheldean Road station and 6 north-west from Newnham, is a plain stone building in the Norman style, with chancel, nave, porch, and tower containing 2 bells and clock and contains west gallery and organ: the seats are, open and all free. The register dates from the year 1817. The living is a vicarage, yearly value £300 with residence and 4 acres of glebe land, in the gift of the Crown and held by the Rev. William Barker, appointed 1866."
http://forest-of-dean.net/index.php/resources/kelly-s-directory-1879/51-east-dean

Pictures of this and other Drybrook Churches may be found here
http://www.forest-of-dean.net/gallery/churches/index2.html
http://www.forest-of-dean.net/gallery/drybrook/pages/page_36.html

In fact a general internet "google" for William Barker immediately gives various hits to posts on this website, plus this site for Holy Trinity Church itself - looks like I should have followed this route first, good to live & learn eh ?!

"In 1866 ill health forced Henry Nicholls to resign and, in the same year, Rev W. Barker took up the task of Vicar of Drybrook. He made it his purpose to see another Church built to serve the nearby community of Lydbrook – the Church of the Holy Jesus. He served this parish for 31 years, making him the longest serving priest that Forest Church has ever had."
http://drybrook.forestchurch.org.uk/about-us/history/the-early-years/

And another William Barker a hundred years later, a descendant perhaps ?
http://drybrook.forestchurch.org.uk/about-us/history/the-post-war-years/

Finally, don't forget general queries can often be solved by carefully searching this forum, which in itself is a huge databse of FoD knowledge across many varied subjects, not just purely FH enquiries, eg
http://www.forum.forest-of-dean.net/index.php?id=29842

Hope this helps, J

The Burial will have taken place at Holy Trinity Church, Drybrook.
Any event which took place at a Church other than Church of England such as Methodist, Baptist, Congregational would have appropriate details shown in the transcript. See Church/Chapel drop down list.

Michael
Admin