hi Sam
Welcome to the forum. Where in Leeds are you? You are correct in that there are not too many places around. I would avoid Wickes, B&Q and Homebase. For hardwoods, I would go to British Hardwoods near Keighley and for other stuff, Arnold Laver are reasonable. Check the prices though, they can be a bit expensive on some, particularly odd lengths of hardwood. Clive walker are ok too, but check stocks. They claim to sell everything and any size but I am not convinced that they hold much on site. For this project, a builders merchant will be good enough, so shop local! William Madden (the Bradley depot) is my preferred builders merchant but it is local to me. Go somewhere that you can see what you are buying and select good straight pieces.
For a work bench, I would use whatever you can get easily and cheaply. Workbenches (at least for me) are a functional item so I would use softwood unless you have a glut of hardwood available at a sensible price. The c16 graded sawn stuff softwood is better than the fast growing CLS. You may also find that the 8x2 is better than the 4x2 and so cut it down to size. WIth that said, I am sure that many benches have been made with CLS in the past without problem.
One thing that you may want to consider is using a solid core firedoor as the top. Saves laminating timber etc and is heavy, dense and reasonably priced- especially if you can pick one up on Facebook or gumtree for not much.
Mark