Smart Casual, Friday casual, whatever you call it. In August there will be a zillion tourists, so it won't really matter.

Jeans are OK, but why bother traveling with them? There are so many other options that are more comfortable and lighter and easier to pack.

Sneakers (or trainers over there) are probably OK for walking around all day, but I wouldn't do them for dinner or anything like that.

Never brought a suit to England unless it was a business trip and required, nor did I ever need one.