Among the Brits, I greatly enjoyed Edmund Crispin's The Moving Toyshop, Dorothy Sayers' Gaudy Night, and Josephine Tey's Miss Pym Disposes and The Daughter of Time. And of course the great Ruth Rendell, though as has been pointed out, she came later. My favorite novels by her are Judgment in Stone, A Dark-Adapted Eye, and Lake of Darkness.
Among Americans, I like Margaret Millar, who wrote from the 1940s until the 1970s . She's not really Golden Age, as her work tends to be more noirish and more interested in psychological depth. She wrote beautifully and was brilliant at plotting, with a special gift for Christie-like misdirection and twists. The one everyone always recommends by her is The Beast in View, but I find that one gimmicky and dated. My favorite Millars are An Air That Kills, Ask for Me Tomorrow, Do Evil in Return, and her early gothic thriller The Iron Gates.
I also adore the work of Millar's husband, Ross Macdonald though again, he's not really Golden Age either. He was one of the foremost practictioners of the hardboiled private eye novel, following in the wake of Chandler and Hammett. He wrote in the genre developed by those writers but with greater psychological depth. He wrote beautifully and his great subject was dysfunctional families, specifically the fucked up children of privilege of California's golden age (1940s through 1970s). My favorite titles by him include The Far Side of the Dollar, The Zebra-Striped Hearse, The Chill, Black Money (which the Cohen brothers tried but alas failed to bring to the big screen), and his early novel The Way Some People Die.
However, my favorite crime novelist of all, and the one I recommend most passionately, is Elisabeth Sanxay Holding. She was an American who wrote crime fiction from the 1920s pretty much until her death in 1955. She's been called the godmother of noir and was clearly a major influence on writers who came later like Patricia Highsmith and Ruth Rendell, as she was writing dark, absolutely riveting novels about about psychologically abnormal criminals long before those other two came along.
Raymond Chandler tended to be stingy in his praise of other crime writers, but not when it came to Holding, whom he singled out as one of his favorites. He called her "the top suspense writer of them all" and said "her characters are wonderful; and she has a sort of inner calm which I find very attractive."
Chandler signed a screenwriting deal and was allowed to choose any novel he wanted to adapt. The one he opted for was The Innocent Mrs. Duff, which imo is Holding's greatest novel. Unfortunately, his script was never made into a film. But another great Holding novel, The Blank Wall, was adapted into a wonderful Max Ophuls film, The Reckless Moment, starring Joan Bennett and James Mason. It was later remade as The Deep End starring Tilda Swinton.
In addition to The Innocent Mrs. Duff and The Blank Wall, my other favorite Elisabeth Sanxay Holding novels include Dark Power, Lady Killer, The Girl Who Had to Die, and Who's Afraid? But really, I've immensely enjoyed every novel by her that I've read (and at this point I've read all but one or two). They are very cinematic and I find it baffling that more of them weren't made into films.
Though her books used to be very hard to find, over the past 20 years or so they've all been brought back into print, often in super-cheap ebook editions. I highly recommend checking her out. You can thank me later.