We are on clay soil too. My neighbour, who digs her patch, dug a small trench around her patch for drainage. It seemed to work for her when we had those weeks of wet weather.
My paths were made with cardboard first, then covered with wood chippings. They felt a Little spongy in the wet weather but were fine to walk on all through the wet months when the rest of the grass paths on the site had standing water for weeks.
Got my wood chip free from a local advert and free cardboard from local shops.
In this dry season, my beds are well mulched with compost and the clay underneath is still moist, though I am only watering vulnerable plants.