Stacks of fun at the London Library and the British Library

Walk into the Reading Room of the London Library – a high-ceilinged room, with Adam-style plasterwork, overlooking St James's Square – and the overwhelming feeling is one of contentment.

The members want to be here rather than anywhere else; most libraries aren't like that. The Bodleian in Oxford is full of undergraduates arranging their next coffee break in loud whispers – anything to get away from Finals revision. The British Library is packed with older students working on that doctorate they wish they weren't doing - cue another four years of arranging coffee in louder, more embittered whispers.

There's serious work being done in the London Library, too; but it's serious work that people are enjoying, not avoiding. And serious work done by serious people: what a frisson you get when you walk through the library's discreet entrance behind Sir Tom Stoppard or, until a few years ago, Sir Isaiah Berlin (both presidents of the Library).

Even if you've just dropped in to flick through the free papers and magazines, you can bask in a little reflected magic from the planet-brained members who've dropped in before you, including Darwin, Dickens, George Eliot, John Betjeman and Kingsley Amis. Or you can rejoice in the twin wonders that are the cheekbones of the actress Natascha McElhone, writing her memoirs in the Reading Room. Lady members may rest their weary eyes on Robert Pattinson, another keen habitué.

The whole place revolves around the importance of books, though, not people. It's right in the heart of clubland, but has none of the puffed-up self-importance of clubs; and there's no danger of being buttonholed by the club bore.

Anyone can join and it doesn't matter what you look like: one larger lady tramps around in trainers and outsized T-shirt; Sir Peregrine Worsthorne's often there in lurid velvet suits of a Robin Hood green. No one gives them a second glance.

The British Library wins hands down when it comes to rare books. But at the London Library you can take the books out, and practically all of them (over a million volumes, making it the world's largest independent lending library) are on the open shelves to browse through. The scholarly, gentle staff are there to help, not hinder. And you can keep books for as long as you like, until another member wants them; there's no such thing as a fine.

Intellectual snobbery is out of bounds, too. As well as scholarly works; Ministers of the Church of Scotland, 1560-1929 is a recent acquisition; you also get the latest novels and biographies. When I joined – a kind godfather gave me a year's membership for my confirmation when I was 15 – I was keen on Elvis Presley and Joyce Grenfell; quite a thrill, then, to find a Grenfell biography on the shelves, which had a picture of her cheek to cheek with... Elvis Presley.

Despite its grand St James's setting, this taste for books over all other things has given the library a comforting feel; not so much of shabby chic, but of basic comfort chic. There is an attic eyrie, where you get tea and instant coffee from a dispenser, for 50p a cup, but that's it as far as catering is concerned. A few years ago, someone suggested installing a plush café, and the late John Wells, the actor and author of the library's history, Rude Words, said, If you want a cup of tea, go to Fortnum & Mason.'

Charitable donations, including a recent £3 million from the Sainsbury family's Monument Trust, have just been spent, not on tea rooms, but on expanding book space and space for reading; £2.5 million from Valerie Eliot, the widow of TS Eliot (a former library president), went on a new building, TS Eliot House.

Admittedly, there was a big row in 2007 at a sudden hike in membership fees, from £210 to £375. Several members resigned; the Library might have been better off slowly increasing the fee over previous years. For anyone who uses the place a lot, though, it's still pretty good value today, at £395 per annum. The £200 fee for 16 to 24 year olds has brought in welcome young blood, too.

In keeping with this functional parsimony, the 1896 building is handsome, but not nearly as imposing as the two 18th-century Palladian palaces on either side. The books are housed in austere stacks' – floor on floor of steel grilles, crammed with books; occasionally you get a tiny electric shock from the metal shelves.

A fair amount of sexual electricity crackles through the stacks, too; two eminent novelists once got down to it in a remote corner of Religion on the fifth floor. Members still debate exactly where; was it in the shadowy section between Pentateuch and Persecutions or that hidden spot between Inquisitions and Indulgences?

Hermione Eyre on the British Library

The British Library is the big mama, the full enchilada. If other libraries are elegant, exclusive churches, then the British Library is the Vatican. It is its own kingdom, a staunch citadel behind a high wall off the Euston Road. It receives all comers, from the professor of philology to the head-scratching novelist. Some come to push forward human knowledge, others to have a cup of tea. You can study the most exalted manuscripts in the world, or work online. Everything is free (thanks to endowments and the government) and everyone is welcome, even, controversially, undergraduates and schoolchildren. It should be a municipal mess but somehow, it works – like a happy beehive, magically, it works.

I don't pretend it's beautiful. From outside, it looks like an out-of-town Tesco, or the red sand castle that Noddy built. It sounds one flat note while next door, Gothic St Pancras plays a whole symphony. It was the life's work of Sir Colin St John Alexander Wilson (known as Sandy') and when it opened in 1997, infamously ten years late and £184 million overspent, Prince Charles described it as looking like an academy for secret police'. But in my view it is more of a Charlotte Brontë heroine – plain but handsome of spirit.

Entering the piazza, you hurry past the ugly Paolozzi sculpture of Newton straining on a thunderbox. Crossing the threshold you relax into an atmosphere of industrious calm. People beat their own footpaths around the building. There is no prescribed way to get anywhere: lift, escalator, ramp, stairs. Whichever route you take, you pass the beating heart of the building, its literal and spiritual centre: the King's Library, George III's personal collection of gold-and-vellum bound volumes which glow inside a vast, dark-tinted glass humidor. It looks ghostly and decorative, but if you loiter long enough beside it you will see it whirr into use as the manuscripts are retrieved for study. The effect is enchanted, like seeing a Van Dyck courtier wink.