But times are changing. The society is in trouble. Money, that most vulgar of commodities, is the problem: it hasn't got as much of it as it once had. In fact it's on its uppers and can no longer afford the lease on its elegant cream stucco pile overlooking Hyde Park.
The grim reaper is taking his toll, too. The RSL's latest newsletter mourns the loss of long-time members such as the historical writers A L Rowse and Geoffrey Trease.
For as long as anyone can remember, its 800 members have gathered periodically to discuss - over sherry, of course - the respective merits of Trollope, Chesterton and even Dorothy Whipple, who was, in her day, as popular as Joanna Trollope.
Alas, literature isn't what it used to be, and in an attempt to spruce up its fusty image, the society has decided to admit scientists to its ranks, in belated recognition that, well, some of them can actually write.
And it has enlisted a band of contemporary writers to deliver what it hopes will be a series of controversial lectures and readings. Stephen Fry, Simon Armitage, Will Self and Philip Hensher are all expected to stir things up, just a little. It's all so different from the good old days with the likes of Samuel Taylor Coleridge, George Bernard Shaw and Thomas Hardy. No one told them they had to be controversial.
The RSL is playing down its struggle to cling on to its past. Its chairman, the biographer Michael Holroyd, admits that money is a problem and that some members are a trifle reactionary. But he believes the society is making progress in its attempts to modernise .
"I remember when we elected Elizabeth David, the cookery writer, a lot of members could not understand why we had," he said. "But when you read her summer pudding recipe you would realise.
"We have had an up and down history, but we have changed a lot in recent times. Our role is still important in promoting literature and in seeing to its well-being."
This is not a view held by Self, who is particularly scathing about its "fellows", many of whom, he understands, have not had a book published in the last 20 years.
"I'm a revolutionary republican so I don't support anything with royal connections. The fact is that most of the royal family cannot even write their own names [so] it is a bit of an oxymoron anyway. The RSL can go the way of all flesh as far as I am concerned."
Jilly Cooper, the doyenne of popular fiction, says it makes little sense to attempt to define what constitutes "literature".
"I would never be invited to tea at the RSL because my novels are best- sellers. But Balzac and Shakespeare all wrote for money," she said. "What is panned when the author is alive could be considered great writing after their death. Even now I'm told that my early romantic fiction is considered classic in the literary sense - I wish they had told me that at the time."
Other writers display a fiercely loyal attitude towards the society. A N Wilson describes it as "the shrine" of literature. Why? "It's run by two of the most beautiful young ladies in London. They make us feel our lives are worth living, and it can be a very lonely life being a writer. It is an excellent organisation and I hope they will resist popular culture. My opinion is that it is a terrible mistake to move with the times."
Yet whatever measures it takes to jazz up its image, one tradition will be retained - new members will continue to sign their application forms with the pen used by Byron.Reuse content