HAH Sainsburys is actually the most expensive of the 3 giants (ASDA, which is basically Walmart...Tesco and Sainsburys).
I shop at Sainsburys because I prefer their healthy living range and wider selection, but Tesco and Asda are cheaper, followed by Sainsburys. I was not trying to lose weight when I first moved over here, but I ended up losing anyways. I was constantly sick for the first 4-6 months
I find British food somewhat bland, if I'm honest. My mother sends me care packages with some of my favourites like Countrytime Lemonade and Sugar Free Jello Pudding. (you can bring these things with you, I also brought along a thingy of Season All seasoning salt and some other goodies like Rice-A-Roni and stuff for when I get homesick)
Its extremely expensive out here, especially in London. I know you'll have a great time anyways! Also, be prepared that things are COMPLETELY different study wise out here. In my first year at University I've had nearly 20,000 words worth of essays completed (and I'm not done yet!). You'll have very little "practical" work in a sense. lol
Good luck! ^_____^