It depends on your tolerance for slower-paced, character-driven narratives. His later works, like 'The Constant Gardener' or 'A Most Wanted Man', are fantastic and more accessible to modern readers because they deal with post-Cold War themes like pharmaceutical corruption and the War on Terror. They're complete standalones. Starting with one of these might feel more immediate and relevant. Then, if you enjoy his prose and moral complexity, you can venture back into the Cold War classics with a better sense of his voice.
I’d actually caution against starting with the very earliest. 'Call for the Dead' is a decent mystery, but it’s not representative of his mature, atmospheric power. You might find it a bit flat. Better to start with the acknowledged peak and work outwards. 'The Spy Who Came in from the Cold' is that peak for the early period. It’s lean, mean, and packs an emotional punch his first two books lack. Hook yourself with his best, then explore the rest.
Don't overlook the short story collection 'The Pigeon Tunnel.' It's non-fiction, essays and recollections. Reading it after you've consumed a few novels is revelatory. You see the real-life incidents that inspired scenes, meet the actual spies he knew, and understand his complicated relationship with his con-man father. It’s like a director's commentary track for his entire career. So my suggested order: two or three major novels (maybe 'Spy,' 'Tinker, Tailor,' and 'Constant Gardener'), then 'The Pigeon Tunnel,' then dive into the rest with new, informed eyes.
What about starting with the latest? 'Agent Running in the Field' or 'Silverview'. They're shorter, crisper, and deal with modern politics (Brexit, the post-Soviet world). His voice is older, wiser, and even more disillusioned. You get the distilled essence of a lifetime of thinking about betrayal. They're not his most complex plots, but they're powerful final statements. Starting with an author's late work can be a unique experience—you see the endpoint first, then trace back to see how they got there.