Gotcha. So if I didn't want an overhang, I should just cut the plywood to replicate the exact dimensions of the MDF, and that'd be fine?
Plywood is only moderately better than mdf when it comes to getting wet, but its not A LOT better. If you want to be ultra safe you should use marine ply. Its a higher grade ply where the glues used are not water soluble. Regardless it too needs a waterproof coating.
A boat repair shop in Leeds maybe?, to see if they can source it and cut it to dimension for you, given that you need probably buy one sheet and its going to be 5 min worth breaking it down with a tracksaw or table saw, and them buying at discount, it might just cost the same as ordering from a specialty store. Ask them to throw a coat of poly or lacquer on it?
Otherwise you're going to want to coat raw normal plywood in an oil based polyurethane and hope that you've done it well. 2 -3 coats would be needed, sanding in between. you'll need mineral spirits to clean your brush. Lacquer is just as good but you'll either need to buy it in a rattle can if available or you need a spraying setup.
all in all it may save you money to have a shop do it. if its a one time thing.
I don't know if you can source oil based poly or lacquer with the strict VOC laws in UK, if you can they're likely very pricey and you need to do it outdoors, if you don't have access to a shop. I can buy it no prob in every home improvement store in the US, but I'm not sure you'll have the same access.
You definitely do not want to do it in your living space and just open the windows. Its not safe, like really not safe, becuase it off gasses for like 24-48 hours and lacquer evaporates fast but the off gas is a propellent... but since its not fine furniture, you can just do it outside and live with the imperfections associated with dust.