The Haytor area has lower, middle and upper car parks, with the visitor centre at the lower one. The roughly 800-metre ascent is from the visitor-centre car park; the rocks are reached on foot. The separate centre has public and disabled toilets, step-free access inside, Blue Badge bays and electric-vehicle charging. Those facilities are useful before or after the climb; the rocky summit approach itself is not step-free.
If you want a gentler alternative, the park’s 2-kilometre return Miles Without Stiles route starts from Haytor middle car park crosses the road and climbs gently beneath the rocks to the quarry and an old tramway viewpoint. The sheltered quarry is a good place to pause. The route is graded “For Some” and has narrow, steep sections through the quarry, so it is not a step-free way to the summit.