From my (now extensive) waterproof short wardrobe:
Cut off army goretex from ebay are great, but the fit for riding isn’t ideal. That said, they cost £10-15, you can cut them to the length you want. When you cut them off, think of a way to narrow the leg, or they will be very flappy. Get sweaty though
Surface Liquistretch shorts are on offer at Evans website – showerproof rather than waterproof, maybe not tough enough for off roading if you fall off or ride through brambles, but very comfy and smart enough to wear down the pub/in the office. Not too swaety
Altura Dryline – like the goretex but 3-4 times the price, great fit on the bike, but prone to sweatiness