Looking to the UK, I can suspend my division between the Universalists and the Unitarians because what few institutional remnants of the Universalists were completely absorbed by the latter. The last Universalist-named church has been gone a half-century. More on that later.
I was struck (again) by how secular London is, and yet how Christianity, through the Establishment, has almost been grandfathered in. The Remembrance Sunday celebrations as I experienced them were deeply moving, but there was something about them that dissatisfied me as a Christian, even as I was able to accept them by proxy into my own patriotic feelings as an American.
So, I'm not quite sure what to make of the 2001 Census statistics (link) that show 71.6% identifying as Christian. (Muslims come next, at 2.7%.)
Of the 59.2 million residents of the United Kingdom, somewhere between 4,000 and 5,000 are Unitarian, and another 3,716 in the Non-Subscribing Presbyterian Church, according to a listing in Reformed Online. (The numbers aren't clear enough to factor out the two churches in the Republic of Ireland.)
If we assume a reasonable sum between the two denominations is 8,500, then we're talking a thin .014% of population (that is, one seventieth of a percent) compared to the current approximate) .08% "shareholding" of the UUA in the United States.
That, and looking at the website of the General Assembly of Unitarian and Free Christian Churches it is clear that many churches don't have a minister (but want one) and cannot or do not worship every week.
Some tough facts.