So this unique residential institution — in contrast to recent American presidents, Gladstone is the only British leader to have established a library — sees itself as a refuge, Mr. Francis said, and one that is being “hugely used at the moment by people who feel the loss of liberal values.”
Four times prime minister, William Ewart Gladstone was first elected to Parliament in 1832, age 23, as a Tory, but he became leader of the Liberal party in 1867, expanding the voting franchise and championing Irish home rule. Whereas his archrival, Benjamin Disraeli, charmed Queen Victoria, Gladstone tended to do the opposite, so much so that the monarch complained that he addressed her as if she were a public meeting.
Yet his scholarly and sober approach may be having a revival.
Reading room visitors increased by 25 percent to 50 percent in each of the first three months of 2017 over last year, and there was an overall 29 percent increase in overnight stays by scholars, writers and others in the same period.
Fund-raising is underway for a $10 million plan to build an auditorium for literary festivals, to improve video capabilities and to upgrade more basic facilities, including the women’s restrooms.
But the idea is to retain the ambience of a place where visitors sometimes feel as if they have stepped from a divided and ill-tempered Britain into a 19th century vicarage.
Sitting in his book-lined office, Mr. Francis, whose formal title is warden, said that as a committed internationalist, Gladstone would have been “very upset” about Britain’s exit from the European Union. He thinks it fair to assume that a politician whose speeches could last four hours would have been unimpressed by President Trump’s Twitter feed.
As for fake news, Mr. Francis added, Gladstone would have been horrified. “I can’t think of any single thing that is more un-Gladstonian,” he said, noting that the statesman prized “deep study and doing your proper research and in some depth, so that you would get all the nuances.”
Evidence of scholarship is all around in this imposing library, built in the first years of the 20th century in Gothic style on the site of the more basic structure — the “Tin Tabernacle” — that Gladstone built in 1889 to house his 32,000 books. Though he turned 80 that year, he helped to move them there in wheelbarrows from nearby Hawarden (pronounced Harden) Castle, his grand country home.
A devout Christian, Gladstone became well known for his rescue work among prostitutes, but his contacts with “fallen women” provoked gossip and speculation. His reputation for intellectual rigor is rarely questioned, however. Mr. Francis recounts how when asked to cut the ribbon to open a flower show, Gladstone read for weeks about flora and delivered a lengthy oration.
Augmented with newer works, Gladstone’s Library now holds more than 200,000 books, journals and periodicals, concentrating on history, literature and theology.
Access is free, which has made the library a popular place of study for local teenagers preparing for exams. It also has 26 bedrooms, with reduced prices for authors, clergy and students, and there is often a writer in residence.
While anyone can reserve a bed, this is not an ordinary hotel. The rooms, while comfortable, are equipped with a retro-style radio, but no TV. Downstairs, in a spacious sitting room, the bar is not staffed; guests are expected to display another Gladstonian quality — integrity — by signing for what they consume.
Along the corridor, under the wooden beams of the large, light and airy main reading room, silence is strictly observed, the only distraction being the thousands of surrounding volumes (one visitor recalls being sidetracked from work by “The Book of British Fish.”)
In addition to his books, Gladstone’s personal papers are here, including his marriage proposal, whose romantic intent was somewhat opaque: It is a letter that includes a sentence of 141 words, with 18 clauses or subclauses.
The library’s many admirers include David Cannadine, the Dodge professor of history at Princeton and a trustee, who describes it as “a very remarkable and special place, both in terms of what it is and what it stands for.”
“People can visit and stay and work in an environment which is simultaneously stimulating, secluded and serene,” he said, adding that “it also embodies those quintessential Gladstonian values of liberalism, tolerance, internationalism, democracy and belief in human rights and the rule of law.”
“In our current climate, they need reaffirming, exploring and celebrating more than ever,” he said.
Another trustee, Patrick Derham, headmaster of Westminster School, described the library as a “magical place,” which, “in an increasingly illiberal world, is even more important now than at any point in its existence.”
Over dinner, the current writer in residence, the novelist Rowan Hisayo Buchanan, put the attraction differently: “When I was a kid, I always wanted to live in a library, then I discovered that there is a library, and you can live in it.”
Liz Simons, a textiles teacher from Cambridge, said she was visiting because of her 18-year-old son’s interest in Victorian history. As a supporter of the right-wing U.K. Independence Party, he may not be typical of Gladstone’s Library users, though she thinks exposure to it may be making him a little more liberal.
Originally, the library was named after the nearby church, St. Deiniol’s, which contains several plaques commemorating the Gladstone family. (William Gladstone, who died at Hawarden Castle in 1898, is buried in Westminster Abbey.)
The library’s warden must be a member of the clergy, and there is a regular communion service at 8 a.m., though Mr. Francis said that there was “no expectation that people go,” and described this as “old-fashioned Anglicanism that goes on like the breathing of the house.”
Mr. Francis remembered being “terribly scornful” that his predecessor stayed in the job for 21 years, yet he is now at the start of his own second decade in the post and seems destined to outdo the record. Not that this means he has become complacent, he added.
“We have a lot of images of Gladstone, and I do find him quite stern,” he said. “You can’t quite loll about doing nothing with Gladstone looking over you. You feel you should be doing something solidly and seriously.”