Not a lot of English military fiction I can think of that is like All You Need is Kill... most are more epic, heroic, and have far fewer discussions of food in them.
Glen Cook's
Black Company series is fantasy milfic, but other than not being scifi it comes close.
David Drake's works, especially the
Hammer's Slammers series, is gritty military fiction alright - but it may be darker than you prefer. His later works (The General series, Belisarius, or the RCN series) are much less dark, while still getting into the dirty details of the military. A LOT of his stuff is closely based on real historical events, updated to scifi environs, with all the relevant details to provide a bonus for history buffs, too, when they recognize stuff.
David Weber has done a bunch of milfic, but it tends to be much more epic, heroic, and light-hearted. Not Vorkosigan levels, but still - not gritty.
John Ringo's books tend to be more epic adventure than pure milfic, but the Council War series is fairly military centric, just... an odd mix of scifi and fantasy, and adventure and milfic. He's an author you need to be careful with, though, some of his other books go off onto religious or gun/porn/gun porn tangents that can ruin an otherwise good story.
All three of these authors (Drake, Weber, Ringo) have some free ebooks available from the publisher, at the
Baen Free Library.
I have a Marko Kloos ebook sitting in my milfic folder, but even looking at the cover, I can't remember much about it. That's another author, though, that does milfic centered on an individual.
One popular milfic author I cannot recommend to you is Tom Kratman. He can write a good military story, but most of his books are political treatises with a story attached. Unless that's what you are looking for, I suggest reading something else.