Pinetree thanks so much.
Now I have the date, and, as predicted, it was a non-conformist church - in fact a Congregational church. A 12 June 1936 article in the same newspaper gives a brief history on p10. The OCR is better for this article:
"OLD MEETING HOUSE
Its Early History
INTERESTING RECORD OF RELIGIOUS PROGRESS
Old Meeting House Congregational Church, Uxbridge, this year celebrates its two hundred and twentieth anniversary, and a few facts relative to its history, which have been prepared by Mrs. F. Tayler, of Wellington-road, Uxbridge, will be read with interest. The history of the church commences in the days of persecution for religious faith to the time when one enjoys full liberty of conscience. The church dates back years, but it was not until 17:6 [1716] that the present building was erected. The earliest records of the origin of the denomination date from :662 [1662], when the Act of Uniformity was passed requiring conformity to the forms, doctrines and ritual of the Established Church. Under this Act two thousand ministers gave up churches, glebes and emoluments. It was then that Puritanism developed into Nonconformity and dissent from the Church of England took place. There were two branches, Independents and Presbyterians. Each section had slightly different ideas as to church government. The two thousand ministers were almost equally divided on this question..."
I also find that BNA search results can send you to the wrong page, and invariably the info is on the previous page and near the crease. Must be a quirk of scanning and possibly some overlap occurs with the adjoining page.
Thanks to your work, I've found both articles via BNA, and similarly to your search, the newspaper in the result has a different title to the original. I've noticed this before and think they use the latest name of a paper since they changed hands and names often and their titles evolved. I guess they go to the head office of a newspaper now, and scan their archives that'll include previous incarnations. You can see why they changed the names with them being so long-winded. Middlesex and Buckinghamshire Advertiser, Uxbridge, Harrow and Watford Journal doesn't really roll off the tongue does it? Presumably an amalgamation of the Advertiser and the Journal at some point, before they split, or shrank, to became the Uxbridge and W Drayton Gazette and ditched their readership from the other areas.
Thanks once again for everyone's help and for Pinetree nailing the details for me.