The honest answer: mostly no
If a lap cat is what you are picturing, a British Shorthair will probably disappoint you, and it is better to know before adoption than after. The typical British Shorthair is affectionate but physically reserved: she will sit beside you at touching distance, lean against your leg, rest a heavy paw on your foot, and purr through an evening of television, yet being lifted off her feet, held in arms, or settled onto a lap usually earns a patient endure followed by a firm departure. All four of this breed's feet prefer contact with a solid surface, and that preference is consistent enough across the breed that breeders warn buyers about it as a matter of routine.
Why this breed dislikes being held
Part of it is build. A British Shorthair is a heavy, dense cat, among the larger shorthaired types, and being held securely takes effort; being held loosely feels unsafe to an animal whose weight is distributed across arms that cannot support her hindquarters properly. Part is temperament: this is a self-possessed breed that likes to choose its positions and keep an exit route, and restraint, however loving, removes both. There is nothing wrong with a British Shorthair who objects to laps, and nothing to fix. Owners who try to train the preference away with repeated forced cuddles usually achieve the opposite, producing a cat who leaves the room when she sees them sit down.
Affection in the British Shorthair's own format
Look for the breed's real vocabulary of attachment instead. A British Shorthair who follows you from room to room and arranges herself nearby, who greets you at the door with her tail upright, who sleeps on the bed at foot level rather than pillow level, and who presents her cheeks for a scratch is showing full devotion in her native format. Many individuals do soften with age and trust: a cat who refused laps at two may drape herself across an adjacent cushion and half onto a trusted person's thigh at six, on her own initiative and her own schedule. Those voluntary moments tend to mean a great deal to owners precisely because the cat was never made to perform them.
Handling her well day to day
Handling sometimes cannot be avoided: carriers, veterinary visits, and moving a cat off a forbidden counter all happen. Make those moments brief, supported, and unceremonious: slide one hand under her chest and the other under her hindquarters, hold her close to your body, move her, and put all four feet down promptly when you arrive. For voluntary closeness, get down to her level instead of bringing her up to yours: sit on the floor for play, groom her where she is lying once she accepts the brush, and keep a folded blanket on the sofa beside you as an open invitation she can take up or ignore. Warn visiting children in advance that this cat is a sit-with cat, not a carry-around cat, and supervise first meetings.
Exceptions and changes worth noting
Breeds describe tendencies, not certainties, and lap-sitting British Shorthairs do exist, particularly among cats raised with gentle handling from kittenhood and individuals from lines selected for soft temperaments. Ask a breeder or rescue honestly how the specific cat responds to laps rather than assuming either way. And as with any breed, treat a change as information: a cat who used to tolerate brief holding and now cries, struggles, or avoids being touched may be in pain, and a cat who suddenly becomes unusually clingy after years of reserve deserves the same attention. Either shift is worth discussing with your veterinarian at or before her next check.
Knowing and recording how your cat likes to be handled protects her with everyone else too: your British Shorthair's Pet Pass on KinsLe holds her verified identity and owner contact details ready to show anywhere, giving anyone helping with her the essential details in one clear place.