I'm going to the Lake District for a day I'm thinking of taking a camera but I do not know whether to buy a waterproof camera or a cheap?

Dslr or bridge camera as I will be going in water and I have a iPhone 7 plus so I'm thinking a dslr or bridge camera would be a waste of money and thinking of buying a go pro should I or not?

The GoPro is a camcorder for shooting video. A camera would be for shooting pictures. They are different.

If you are just going to splash on the water, a Pentax KS2 dSLR would be great. It can tolerate getting wet, muddied or placed on the sand but it can't be submerged. If you want a camera that can dive with you underwater, look for a Ricoh/Pentax WG series camera.

For under $150 you can buy a waterproof, drop proof and freeze proof camera which also has a 3x optical zoom. That camera is the Nikon Coolpix S33. The iPhone has none of these features. The GoPro has only a wide angle lens and is specifically designed for shooting POV video.